9.4 Board Game Sales
A small company is selling a new board game, and they need to know how many to
produce in the future.
After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand
games; and after 36 months, they sold 15 thousand games.
1. Could this information be reasonably estimated using a single linear model?
2. If so, use the model to estimate the number of games sold after 48 months. If not,
explain your reasoning.
By using slope of a curve, it can be calculated that
This information cannot be estimated by a single linear model
What is slope of a curve?
Slope of a curve at a point is the tangent of the angle that the tangent to the curve at the point makes with the positive direction of x axis.
The sale of the board game is as follows-
After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand games; and after 36 months, they sold 15 thousand games.
The curve passes through (12, 4000), (18, 7000) and (36, 15000)
Slope of curve passing through (12, 4000) and (18, 7000) = [tex]\frac{7000 -4000}{18 -12}[/tex] = 500
Slope of curve passing through (18, 7000) and (36, `15000) = [tex]\frac{15000-7000 }{36 -18}[/tex] = [tex]\frac{4000}{9}[/tex]
As the slope is not the same, this information cannot be estimated by a single linear model
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The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a function? Edge Length, x Surface Area, y 1 6 2 24 3 54 4 96 A graph of a curve on a coordinate plane that goes up and to the right with edge length in units on the x axis and surface area in square units on the y axis. The curve begins at the origin and passes through the points 1 comma 6 and 2 comma 24 and looks like the right half of a U.
We infer that x and y's relationship is a non-linear function as a result. The relationship between x and y is a non-linear function.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
Here,
Edge Length, x Surface Area, y
1 6
2 24
3 54
4 96
Because each input value has one and only one output value, the data in the table unmistakably indicate a function. In other words, the x values are not repeated.
Additionally, it is evident from the table numbers and the graph that the function is not linear because the graph is not a straight line. Additionally, the largest power over the x variable(s) in a cubic function is 3. It is not a linear function, therefore.
As a result, we draw the conclusion that x and y's relationship is a non-linear function.
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In the picture below.
Answer:
∠ GFC = 70°
Step-by-step explanation:
∠ BFE and ∠ CBF are alternate angles and are congruent, that is
∠ BFE = 37°
∠ BFE , ∠ BFC and ∠ GFC lie on a straight line and sum to 180° , then
37° + 73° + ∠ GFC = 180°
110° + ∠ GFC = 180° ( subtract 110° from both sides )
∠ GFC = 70°
A bowl contains x cups of milk. Mrs. Medina used 2.15 cups for her cereal. The bowl now contains 1.30 cups of milk. How much milk was in the bowl before Mrs. Medina needed some for her cereal?
0.85 cups
3.45 cups
1.30 cups
2.15 cups
You have one penny, one nickel, one dime, and one quarter. How many different amounts of money can you make using
one or more of these coins?
Answer:
15
Step-by-step explanation:
To find the total number of combinations you can make with these four coins, we have to do 2 to the power of the total amount of coins. This because each coin has two choices: to be included in the combination or not. There are 4 total coins, and 2^4 is 16. There are 16 total combinations. But since one of those possibilities are that none of the coins are included, we subtract 1 from the total, and get 15. There are 15 combinations with 1 or more coins, which each give us different amounts.
18.
Kara solved the following absolute value equation incorrectly. Find and fix her
mistake. Explain what she did wrong.
|- 2x + 6 + 10 = 2
-10 -10
2x+6=-8
-6 -6
-2x = -14
-2
-2
X = 7
|- 2x + 61
{7, - 1}
= -8
2x+6=8
-6 -6
-2x = 2
-2 -2
x = -1
Kara erred when she answered the equation 2x + 6 = -8. Instead, she should have solved the equation 2x + 6 = 8 because it relates to the second situation (where -2x + 6 + 10 is smaller than 0).
Kara made a mistake when solving the equation |- 2x + 6 + 10| = 2. The correct steps to solve this equation are as follows:
First, we need to find the value of -2x + 6 + 10. To do this, we need to remove the absolute value bars by considering two cases:
a. If -2x + 6 + 10 is greater than or equal to 0, then the absolute value is equal to -2x + 6 + 10.
b. If -2x + 6 + 10 is less than 0, then the absolute value is equal to the negative of -2x + 6 + 10.
In the first case, we have -2x + 6 + 10 = 2. Solving this equation gives us x = -1.
In the second case, we have -(-2x + 6 + 10) = 2. Solving this equation gives us x = 7.
Therefore, the solution to the equation |- 2x + 6 + 10| = 2 is x = {7, -1}.
She made a mistake when she solved the equation 2x + 6 = -8. She should have solved the equation 2x + 6 = 8 instead, because this is the equation that corresponds to the second case (where -2x + 6 + 10 is less than 0).
As a result, Kara got the wrong value for x and included the incorrect solution {7, -1} in her final answer.
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alis teacher plotted the numbers 1/2 and 2/3 on the number line. She asked ali to find and plot a rational number between these two numbers in a number line, Can you help Ali in plotting a rational number between them on a number line?
Yes, there are many rational numbers that can be plotted between 1/2 and 2/3 on the number line. Here are a few examples:
1/2 + 1/6 = 5/6: This rational number is greater than 1/2 and less than 2/3.
2/5: This rational number is also greater than 1/2 and less than 2/3.
1/3: This rational number is halfway between 1/2 and 2/3.
To plot a rational number on a number line, you can start by drawing the number line and marking off the positions of 1/2 and 2/3. Then, you can locate the position of the rational number you are trying to plot by dividing the distance between 1/2 and 2/3 into equal segments and finding the position of the rational number within those segments. For example, if you wanted to plot 5/6, you could divide the distance between 1/2 and 2/3 into six equal segments, and then mark the fifth segment as the position of 5/6 on the number line.
............ i need help past due
Answer from left to right: 48, 80, 4.5, 160
Step-by-step explanation:
What is 3+3+3x4
Enjoy the points :)
Saying a thanks would be nice
Answer:
18
Step-by-step explanation:
awwww this is so sweet of you! you see this is the type of people we need in the world, kind people like you just wanting to help, thats why I answer questions on brainly not for the points and popularity but to help people out, thank you! <33333
Answer:
If the x is a Times then its 18 but if its not its 3x4+6
Step-by-step explanation:
show steps / why your answer is correct please which equation defines the graph of y=x3 after it is shifted vertically 5 units down and horizontally 4 units left
The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
What is a graph?A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.
For k=- 5, y=f(x) + k represents a vertical shift down.
For h=4, the horizontal shift left is y=f(x+h).
Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
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Find the interquartile range of the data set shown
5 8 12 12 17 18 20 22 23
what is the interquartile range
Answer:
8
Step-by-step explanation:
12 is quartile 1 and 20 is quartile 3. 20 - 12 = 8
Answer: 8
Step-by-step explanation:
2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Angle T R V is 95 degrees.
mAngleSRW =
°.
The measure of the angle ∠SRW will be 95°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
2 converging lines are shown. A line with focuses TRW converges a line with focuses SRV at point R. The angle ∠TRV is 95 degrees.
The angle ∠TRV and the angle ∠SRW are opposite angles. Then we have
∠TRV = ∠SRW
∠SRW = 95°
The measure of the angle ∠SRW will be 95°.
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please help me.
question in screen shot
Answer:
x = -1
Step-by-step explanation:
First of all, we must find the value of what's inside the parentheses.
14 ÷ -2/3 =
14/1 x -3/2 = -42/2 = -21
That means the equation is now:
-21 = 6x - 15
+15 +15
-6 = 6x
-1 = x
Question 9(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the distance between the points (-3, -6) and (5,0).
©22 units
10 units
8 units
05 units
Therefore, the distance between the points (-3, -6) and (5,0) is 10 units. This is option A.
What is the distance formula?A mathematical procedure called the distance formula is used to calculate the separation between two locations on a plane. The Pythagorean theorem, which asserts that the square of a distance between two locations is equal to the sum of the squares of a difference in their coordinates, is where the formula is derived from.
To utilise the distance formula, you must first have the coordinates of the two places. These coordinates are usually expressed as (x1, y1) and (x2, y2), where x1 and y1 stand for the coordinates of the first point and x2 and y2 stand for the coordinates of the second point, respectively.
d = √((x2 - x1)^2 + (y2 - y1)^2)
How to solve?
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((5 - (-3))^2 + (0 - (-6))^2)
= sqrt((8)^2 + (6)^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
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please help with this nothing hard help is appreciated
The dotted line represents that the region is strictly less than the equation of the line.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The dotted line shown in the graph and the yellow region described by the equation of a line is the region that is strictly less than the given line.
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A metal block has a mass of 5kg, correct to the nearest 50 grams. find the upper bound
Therefore, the solution to given problem is the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]
What is density?The substance's density is defined as its mass per unit of volume. Although the Latin letter D can also be utilized, the most popular density symbol is. In mathematics, density is calculated as mass divided by volume:
Here,
Given : mass =5kg
volume = 1.84 x [tex]10^{-3}[/tex]
thus, density = mass/volume
we apply density formula , we get
density = 5/ 1.84 x [tex]10^{-3}[/tex]
density =2717.4 kg/[tex]m^{3}[/tex]
Therefore the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]
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what is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?
The answer to this Question based on probability is discussed below
What is probability of a event?
It is just defined as number of favourable outcomes divided by the total number of outcomes.
Solution:
First of all we need total number of events here as we know probability of sample space is 1 only. hence lets assume there are P elements in sample space and Solving more than number of expected puzzles in 5 minutes is 1 favourable case.
Hence probability will be 1/P where P is no of elements of sample space.
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In exchange for a $300 million fixed commitment line of credit, your firm had agreed to do the following:
1. Pay 1. 85 percent per quarter on any funds actually borrowed
In exchange for a $300 million fixed commitment line of credit, your firm had agreed to pay an up-front commitment fee of .130 percent of the amount of the line.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent.
Here,
Your company had agreed to pay an upfront commitment fee equal to.13% of the line's value in exchange for a $300 million fixed commitment line of credit.
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Jesse’s luggage weighs 55 pounds. The airline says that luggage cannot be more than 30 kilograms. Is her luggage under this limit? Explain.
Answer: yes, her luggage is under limit
Step-by-step explanation:
1 kg = 2.2 pounds
Take 55 divided by 2.2 = 25 kg
25 < 30
Her luggage is under the limit
3. Marcus Hatfield earns an annual salary of $43,500 working for a natural
history museum. He is single, and his exemptions total $2,000. He pays
$954.50 in state taxes each year. What is the tax rate for his state?
The Rate of Tax for his state is 2.3%.
What is tax rate?
The ratio at which a business or individual is taxed in a tax system is known as the tax rate. Statutory, average, marginal, and effective tax rates are some of the ways that are used to present them. The terms inclusive and exclusive can be used to present these rates when applied to a tax base.
Annual Salary of Marcus Hatfield is = $43500
His Exemption from the tax is = $2000
He pays tax on the remaining amount i.e.
$43500 - $2000 = $41500.
His contribution toward the tax is $ 954.50,
Let the Rate of tax is x, thus
[tex](\frac{X}{100} *41500) = 954.50\\ x = \frac{95450}{41500} \\x = 2.3[/tex]
Thus, the rate of tax is 2.3% of his salary.
Hence, the Rate of Tax for his state is 2.3%.
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What is the y-intercept of this line? y=-5x -3 b= [?]
answer:
b=-3
step-by-step explanation:
the equation's format is y=mx+b so b is -3. you can also figure this out if you plug y in as 0. hope that helps!
Decrease £250 by 15%
Answer:
£212.5
Step-by-step explanation:
15% of 250 = 37.5
250 - 37.5 = 212.5
Describe the end behavior, determine whether it’s a graph of an even or odd degree function, determine the sign leading coefficient
Answer:
Right and Left: Negative Infinity
Even Function
Negative Leading Coefficient
Step-by-step explanation:
First of all, both ends of the graph go down to negative infinity. As a result of this, we can determine that the sign of the leading coefficient was also negative. The graph is even because it shifts directions thrice and both ends of the graph go in the same direction.
Write a pattern rule that uses algebra to describe each pattern. a) 7, 14, 21, 28, 35, 42,
HELP!!!!
Answer:
as u can see the pattern is going up by 7.
Step-by-step explanation:
#9 find the converse, inverse, and contrapositive to the following conditional statement: walking in front of a moving car is dangerous to your health
The converse of statement is “If dangerous to your health then walking in front of a moving car”.
The inverse of statement is “If not dangerous to your health then not walking in front of a moving car”.
The contrapositive of statement is “if not walking in front of a moving car then not dangerous to your health."
What is the conditional statement?The definition of a conditional statement refers to its two essential parts, the hypothesis (if) and the conclusion (then).
The given conditional statement is
"walking in front of a moving car is dangerous to your health."
The converse is “If dangerous to your health then walking in front of a moving car”.
The inverse is “If not dangerous to your health then not walking in front of a moving car”.
The contrapositive is “if not walking in front of a moving car then not dangerous to your health."
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find (9.3x106) + (1.8x104) express your answer in scientific notation
Answer: here is your answer
Step-by-step explanation:
(9.3 × 10^6) + (1.8 × 10^4) is 93.18E+5.
(9.3 × 106) + (1.8 × 10^4)
(9.3 × 106) + (0.018 × 10^6)
(9.3 + 0.018)× 10^6
(9.318)× 10^6
scientific notation
(93.18E+5)
Adrian started a small business making custom t-shirts. His profit the first month was -$20. If this continues for the next 3 months, what would his profit be?
(-20)(3)
(-20)(-3)
(-20) + 3
(-20) - 3
Answer:
His profit would be (-20)*3 or -60 $
Step-by-step explanation:
First month profit = -20 $
if the next three months will be the same, then:
(-20)*3
-60 $
Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
To view the representation of graph of check the attached image.
What is called graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Given that ;
Stewart's overdue assignment = 36
Per day he complete 4 overdue assignments.
To find : In how many days he complete all the overdue assignments
To complete 36 overdue assignments = 36/4
= 9 days
Therefore, In 9 days he complete all the overdue assignments
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Math test!! Please help
1. 12*2/ 3
A. 8
b. 16
c.18
D.24
2. 4/5 *9
a. 9 4/5
b. 8 4/5
c. 8 3/5
d. 7 1/5
3. What is the product of 10 and 3/4? give your answer in lowest terms
a. 7 1/4
b. 7 2/3
c. 7 1/3
d. 7 1/2
4. Andie is making bags of candy to give to her 7 friends. she is putting 2/3 of a pound of candy in each bag. How many pounds of candy will she need in order to fill all 7 bags
a. 4 1/3
b. 4 2/3
c. 4 1/6
d. 4 3/4
5. A recipe calls for 3/4 cup of flour. How many cups of flour will u need to make three batches of the Recipe.
A. 2 3/4 cups
b. 2 1/3 cups
c. 2 1/4 cups
d. 2 1/2 cups
6. Evaluate the expressions, Then select all the expressions that are greater then four.
A. 7 * 5/6
b. 4/5 *10
c. 3/8 *9
d. 1/2 *12
7. Evaluate each expression, then select all the expressions that are whole numbers.
A. 9* 2/3
b. 4/5 *7
c. 7/8 *2
d. 25 * 2/5
Answer:
1. (A.)
2.(D.)
3.(D.)
4.(A.)
5.(A.)
6. (B.) & (D.)
7. (A.), (D.)
Step-by-step explanation:
Trust
Write y=-3/4x+7 in standard form
-28 is the standard form of the equation.
How do you format a sentence in standard form?Ax+By=C is the formula for a linear equation. You must place the x and y on the same side of the equal sign and the constant on the other side in order to convert an equation in slope-intercept form (y=mx+b) to standard form. Terms can be moved using inverse procedures.
The standard form of a linear equation is
Ax+By=C A x + B y = C .
y=-3/4x+7 in standard form
Multiply both sides by 4 .
4y=4(3.4x+7) 4 y = 4 ( 3 4 x + 7 ).
3x - 4y = -28
-28 is the standard form of the equation.
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