14. Catherine found that as she increases the price of a chocolate bar, the number of sales per week decreased.
Week Number of Sales
1 149
2 143
3 137
4 131
5 125
a. Write a formula for the arithmetic sequence that represents the number of sales per week.
b. Explain how you could use the information to predict the number of sales for the eighth week.
Answers
Using an arithmetic sequence, we have that:
a) The formula is: \(a_n = 149 - 6(n - 1)\)
b) With n = 8, we have that 107 bars were sold in the eight week.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
\(a_n = a_1 + (n - 1)d\)
In which \(a_1\) is the first term.
Given the table, the first term and the common difference are, respectively, given by:
\(a_1 = 149, d = 143 - 149 = -6\).
Hence the equation is:
\(a_n = 149 - 6(n - 1)\)
Then, the number of sales in the 8th week is given by:
\(a_8 = 149 - 6(8 - 1) = 107\)
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Related Questions
PLZ HELP ITS DUE TODAY!!!!
Show work!!!
Answers
Answer: -7/20
Explanation; look at the imagine attached
26. My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CAN- NOT be the correct combination of my brother's lock? (A) 8560 (B) 3015 (C) 4906 (D) 1893 (E) 6348 0782 Activate Windows
Answers
Answer:
A
Step-by-step explanation:
The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.
a/5 divided by 3/10a if a does not equal 0? What is the answer?
Answers
Answer:
The answer is \(\frac{2}{3}\)
Step-by-step explanation:
When we divide two fractions, we multiply the numerator by the inverse of the denominator. So
\(\frac{\frac{a}{5}}{\frac{3a}{10}} = \frac{a}{5} \times \frac{10}{3a} = \frac{10*a}{5*3a} = \frac{10a}{15a} = \frac{2}{3}\)
The answer is \(\frac{2}{3}\)
what is the GCF of 36,72,48,
Answers
Answer:
12
Step-by-step explanation:
12 can go into all of the numbers above & is the greatest common factor of the numbers above.
Microeconomics
The total cost function of a monopolist is (Q) = 3Q. The inverse demandfunction for
the monopolist’s products is P (Q) = 12 − Q.
A. find the profit-maximizing level of price and output
B. Find the maximum profit of the firm at an equilibrium price level
Answers
Step-by-step explanation:
A. To find the profit-maximizing level of price and output, we need to find the equilibrium point where the marginal revenue equals marginal cost.
The marginal cost of production is the derivative of the total cost function: MC = dC/dQ = 3.
The marginal revenue is the derivative of the inverse demand function: MR = dP/dQ = -1.
So at the profit-maximizing level of output, MC = MR.
3 = -1
Q = 6
Then we can substitute Q = 6 back into the inverse demand function to find the price:
P (Q) = 12 - Q
P (6) = 12 - 6
P = 6
So the profit-maximizing level of output is 6 units at a price of $6.
B. To find the maximum profit of the firm, we need to calculate the total revenue and the total cost at the profit-maximizing level of output.
The total revenue is the product of the price and the quantity:
TR = P * Q
TR = 6 * 6
TR = 36
The total cost is given by the total cost function:
TC = C (Q)
TC = 3 * Q
TC = 3 * 6
TC = 18
So the maximum profit is the difference between the total revenue and the total cost:
Profit = TR - TC
Profit = 36 - 18
Profit = 18
The maximum profit of the firm is $18 at an equilibrium price level of $6 and an output level of 6 units.
1. Circle the figure you would use to make the Escher‐like tessellation given,
Answers
Answer:
C.
Step-by-step explanation:
Answer:
I got C.
Step-by-step explanation:
(It's on my math paper)
find the coordinates of B' after a reflection across the x-axis. show your work
Answers
Answer:
B'(8, 6)Step-by-step explanation:
Coordinates of point B = (8, -6)
Reflection across the x-axis results in:
(x, y) → (x, -y)Coordinates of B'
(8, -6) → (8, -(-6)) = (8, 6)Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
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help plsss
rotate tuv 90 degrees clockwise around the origin
Answers
Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)
Step-by-step explanation:
IV.Activity
Which items can you buy for 2000?
(A) Bat and Helmet
(B) Glove and Bat
(C) Bat and Pad
(D) Helmet, Glove and Pad
Answers
Answer:
bat and pad is correct answer
You are given that z > 2. Write an inequality for each expression.
a) 2z+ 9
b) 3(z - 4)
c) 4+2z
d) 5(3z-2)
Answers
a) The inequality for the expression 2z + 9 is 2z + 9 > 13.
b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The inequality for the expression 4 + 2z is 4 + 2z > 8.
d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.
a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:
2z > 2 * 2
2z > 4
Adding 9 to both sides:
2z + 9 > 4 + 9
2z + 9 > 13
Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.
b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:
3z - 3 * 4
3z - 12
Since we are given that z > 2, we can substitute z > 2 into the expression:
3z - 12 > 3 * 2 - 12
3z - 12 > 6 - 12
3z - 12 > -6
Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:
4 + 2z > 4 + 2 * 2
4 + 2z > 4 + 4
4 + 2z > 8
Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.
d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):
5 * 3z - 5 * 2
15z - 10
Considering the given inequality z > 2, we can substitute z > 2 into the expression:
15z - 10 > 15 * 2 - 10
15z - 10 > 30 - 10
15z - 10 > 20
Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.
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Kim drew a map of the Mississippi River. The scale was 5 centimeters represents 120 miles. The actual length of the Mississippi River is 2,320 miles. Approximately what is the length in centimeters of the Mississippi River on the map?
Answers
Considering the definition of scale, the length of the Mississippi River on the map is 96.667 cm.
Definition of scaleThe scale of a cartographic representation, or map scale, is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map.
Scale is the relationship between a real object (for example, the surface of the Earth or a portion of it) and the representation that is made of it.
The scale is represented as a fraction as follows: measured on the map/measured in reality
Length of the Mississippi River on the mapIn this case, you know that:
The scale was 5 centimeters represents 120 miles. The actual length of the Mississippi River is 2,320 miles.Considering the definition of scale, you can calculate the length of the Mississippi River on the map as follow:
5 cm/ 120 miles= measured on the map/2320 miles
(5 cm/ 120 miles)× 2320 miles= measured on the map
96.667 cm= measured on the map
Finally, the length of the Mississippi River on the map is 96.667 cm.
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what is the equation to this
Answers
The equation of the line passing through the points (3.5, 10) and (0, 3) is:
y = 2x + 3
Given is a line passing through points (3.5, 10) and (0, 3) we need to find the equation of the line,
The slope-intercept form of a linear equation can be used to determine the equation of a line passing through two points:
y = mx + b
where 'm' is the slope of the line, and 'b' is the y-intercept.
First, let's find the slope (m) using the two given points (3.5, 10) and (0, 3):
m = (y2 - y1) / (x2 - x1)
m = (3 - 10) / (0 - 3.5)
= -7 / -3.5
= 2
Now that we have the slope, we can use it to solve for the y-intercept 'b' by adding it to the equation together with one of the supplied locations. Use the example from point (3.5, 10):
10 = 2(3.5) + b
10 = 7 + b
b = 10 - 7
b = 3
Hence, the equation of the line passing through the points (3.5, 10) and (0, 3) is:
y = 2x + 3
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What is the volume of the following rectangular prism? 3 1/3 1 2/5
Answers
Area of rectangular prism: Base x Height.
so 3x1/3x2/5=0.4 0r 2/5
Factor:j) x(x+2) + y (x + 2) - 5(x + 2)k) 5y2 - 10y3l) ax + ay + az
Answers
Given:
\(x\left(x+2\right)+y(x+2)-5\left(x+2\right)\)Required:
We need to factorize the given expressions.
Explanation:
\(x\left(x+2\right)+y(x+2)-5\left(x+2\right)\)The common multiple in all terms is (x+2).
Take out the common term (x+2).
\(x\left(x+2\right)+y(x+2)-5\lparen x+2)=(x+2)(x+y-5)\)Final answer:
\(\begin{equation*} (x+2)(x+y-5) \end{equation*}\)K)
Given:
\(5y^2-10y^3\)
Explanation:
The given expression can be written as follows.
\(5y^2-10y^3=5y^2-5\times2\times y^2\times y\)\(5y^2-10y^3=5y^2-5y^2\times2y\)\(\text{ The common multiple in all terms is }5y^2.\)\(\text{ Take out the common term }5y^2.\)\(5y^2-10y^3=5y^2(1-2y)\)Final answer:
\(5y^2(1-2y)\)l)
Given:
\(ax+ay+az\)Explanation:
\(\text{ The common multiple in all terms is }a.\)\(\text{ Take out the common term }a.\)\(ax+ay+az=a(x+y+z)\)Final answer:
\(a(x+y+z)\)What is the probability that either event will occur? 17 A 29 B 14 P(A or B)
Answers
The probability that either event A or B will occur is 43/60
Getting probability value :Using the parameters given
n(A) = 29
n(B) = 14
Total number of events = 29+17+14 = 60
The probability of each event :
P(A) = 29/60
P(B) = 14/60
P(A or B ) = P(A) + P(B)
P(A or B ) = 29/60 + 14/60
P(A or B ) = 43/60
Therefore, the probability of A or B is 43/60
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find inverse of f(x)= 5x+ln(x-2)
Answers
Answer:
y = 5 x + ln ( x − 2 )
what is b in this equation
b÷4+16=48
Answers
Answer:
b=128
Step-by-step explanation:
b÷4+16=48 isolate b
b÷4= 32
b= 128
Answer:
b=128
Step-by-step explanation:
rewrite
1/4b + 16 = 48
multiply both sides by 4
b + 64 = 192
move constant to the right and change he sign
b = 192-64
subtract
b = 128
What is the volume of a sphere that has
a radius of 11.5 units?
Answers
Answer:
6370.63 is the volume
Step-by-step explanation:
V=4
3πr3=4
3·π·11.53≈6370.6263
Find the length of the third side. If necessary, write in simplest radical form.
2√34, 6
Answers
The length of the third side is 2√34 + 6.
We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.
Let x be the length of the third side. Then we have:
2√34 + 6 > x
Subtracting 6 from both sides, we get:
2√34 > x - 6
Adding 6 to both sides, we get:
x < 2√34 + 6
Therefore, the length of the third side must be less than 2√34 + 6.
To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:
2√34 + 6 = x
If this is true, then the given sides can form a triangle.
Simplifying the equation, we get:
x = 2√34 + 6
The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.
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Which of the following is a solution to this inequality?
y<2/3x+2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
Answers
Answer:
(d) (1, 2)
Step-by-step explanation:
You want to know which of the given points satisfies the inequality.
GraphWe find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)
__
Additional comment
Another way to choose the answer is to try each of the points in the inequality.
If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).
You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.
7. Triangle MNQ is similar to triangle MOP. N 30 cm 9 cm M 0 12 cm P M M 24 cm Find the length of NQ. O A. 9.6 cm O B. 15 cm O C. 60 cm O D. 22.5 cm Please help!!! :( It is due today !!!
Answers
If the triangles MNQ and MOP are similar, then you know that the corresponding sides are at the same ratio. Because of this property, we can determine that:
\(\frac{MN}{MO}=\frac{MQ}{MP}=\frac{NQ}{OP}\)We know the measure of the corresponding sides MQ=12cm and MO=24cm, and the measure of the corresponding side to NQ, using these measures we can calculate NQ as follows:
\(\begin{gathered} \frac{MQ}{MO}=\frac{NQ}{OP} \\ \frac{12}{24}=\frac{x}{30} \\ 30(\frac{12}{24})=x \\ x=15 \end{gathered}\)Side NQ measures 15 cm
The correct option is B.
Express 34% as a fraction in simplest form.
34/100
8/25
17/50
3/4
Answers
Did you just state the answer? Because it seems like you just answered the question for us.
You have several numbers in a data set: 5, 7, 9, 11, 13, 15, 17. What is the z Score for the number 15? (the SD is 4.32)
Answers
The value of the z-score for the number 15 in a data set is 0.93.
Define z-score.
A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.
You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.
∴ z = (x – μ) / σ
Given:
σ = 4.32
x = 15
Data set: 5, 7, 9, 11, 13, 15, 17
So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7
= 77/7
μ = 11
z = (x – μ) / σ
= (15 - 11)/4.32
= 4/4.32
z = 0.93
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11 x 9/10
an explantion would be very nice i start school tomorrow and still havent finished my summer homework.
Answers
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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write the prodect 7 times 7 times 7 times 7 in exponential form
Answers
Answer: 7⁴ I believe
Evaluate the function.
f(x) = -x2 + 6x + 4
Find f(-7)
PLSS HELP TODAY IS THE LAST DAY
Answers
Answer:
-87
Step-by-step explanation:
-(-7^2) + 6(-7) + 4
-49 -42 + 4
-87
Answer:
f(-7) = -3
Step-by-step explanation:
The exponentiation x^2 must be done before multiplication by the coefficient -1.
Substituting -7 for x, we get:
-(-7)^2 + 6(-7) + 4 = f(-7)
Then f(-7) = -49 + 42 + 4, or
f(-7) = -3
A baby that is 18 inches long receives a score of
.
Answers
Answer:
-2
Step-by-step explanation:
A recent research show that only 40% of the customers are willing to pay more for the service. Now we have selected 10 customers randomly. What are the expected value and standard deviation
Answers
Answer:
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
40% of the customers are willing to pay more for the service.
This means that \(p = 0.4\)
Now we have selected 10 customers randomly.
This means that \(n = 10\)
What are the expected value and standard deviation
\(E(X) = np = 10*0.4 = 4\)
\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55\)
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.