Todd is attempting to predict how much money his furniture company will make based on the amount raw materials the company currently has at its disposal. The average profit from the sale of 1 piece of furniture can be expressed as 3x + 1 and the average number of pieces of furniture that can be made using the current supply of raw materials can be expressed as 3x - 1. What polynomial function can Todd use to calculate the average profit?
Todd can use the polynomial function [tex]9x^2 - 1[/tex] to calculate his average profit based on the amount of raw materials his furniture company currently has.
Explanation:The question is asking for a polynomial function that Todd can use to calculate the average profit based on the amount of raw materials the company currently has. To find this, Todd will need to multiply the profit from each piece of furniture (3x + 1) with the amount of furniture he can produce (3x - 1). Thus, the polynomial function will be [tex](3x + 1)(3x - 1)[/tex]. After simplifying we get [tex]9x^2 - 1.[/tex] So this is the polynomial function that Todd can use to predict his average profit.
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The sum of 2 numbers is 22. three times one number is equal to ten more than the other. find the numbers
A spinner has 6 parts numbered 1–6. If the result is 1 or 6, a player wins the number times $10.00. On the other hand, if the result is 2–5, then the player loses the number times $5. What can you say about this game?
The probability of winning is higher than that of losing.
The probabilities of winning and losing are equal.
The probability of losing is higher than that of winning.
There is not sufficient information about the game.
2 numbers win
4 numbers lose
so answer would be The probability of losing is higher than that of winning.
Answer:
Option C
Step-by-step explanation:
We are given that a spinner has 6 parts numbered 1-6.
If the result is 1 or 6 then a player wins the number times $10.00.If the result is 2-5 then the player loses the number times $5.
Number of cases when the player wins number times $10.00=1 or 6=2
Number of cases when the player loses the number times $5=2,3,4,5=4
Total number of cases =6
Formula for finding probability
P(E)=[tex]\frac{Number \;of\; favourable\; cases}{Total \; number\; of \; cases}[/tex]
Applying this formula
The probability of wining=[tex]\frac{2}{6}[/tex]
The probability of wining=[tex]\frac{1}{3}[/tex]
The probability of wining=0.33
The probability of losing=[tex]\frac{4}{6}[/tex]
The probability of losing=[tex]\frac{2}{3}[/tex]
The probability of losing=0.66
Hence, the probability of losing is higher than that of winning.
Therefore, option C is true.
Great Mountain Park: All day pass: 20.25 Mountain coaster: 4.50 Tilt a Loop: 4.75 Water coaster: 4.00 Fast drop: 3.50 Swing a Ling: 2.75 Merry go Around: 2.50. Prices at the Great Mountain Park are shown in the table Above. You and three friends are going to the park on the weekend. Three of you decide to get the all day pass. The other is just going to ride the Mountain coaster twice, the water coaster once and the fast drop once. IF you pay for everyone, what change will you get back from a 100 bill
Answer:
the answer is
22.75
The formula for the circumference of a circle is C =2 pi r.
Find the circumference of a
circle with a radius of 2 cm.
A. 12.56 cm
B. 12.56 cm^2
C. 6.28 cm
D. 6.28 cm^2
E. 12.00 cm
If the sum of five consecutive even integers is t, then, in terms of t, what is the greatest integer?
The greatest integer is t/5 + 4 in terms of t.
What are Integers?Integers are numbers which includes the set of natural numbers, o and the negatives of all those natural numbers.
Set of integers are usually denoted as Z.
Let the first even integer be x.
Then the consecutive even integer is x + 2.
Integers are x, x + 2, x + 4, x + 6 and x + 8.
Given, sum of five consecutive even integers is t.
x + x + 2 + x + 4 + x + 6 + x + 8 = t
5x + 20 = t
5 (x + 4) = t
x + 4 = t / 5
Greatest integer is x + 8.
x + 8 = (x + 4) + 4 = t/5 + 4
Hence the greatest integer is t/5 + 4.
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Decide which of the two points lies on the graph something line
X+3y=-2
A. -6,6
B. 4,-2
Which description matches the graph of the inequality y ≥ |x + 2| – 3? a shaded region above a solid boundary line a shaded region below a solid boundary line a shaded region below a dashed boundary line a shaded region above a dashed boundary line
Final answer:
The graph of the inequality y ≥ |x + 2| − 3 is represented by a shaded region above a solid V-shaped boundary line that has its vertex at the point (-2, -3).
Explanation:
To determine which description matches the graph of the inequality y ≥ |x + 2| − 3, it is essential to understand the properties of the inequality and the properties of absolute value functions. The absolute value function |x + 2| creates a V-shaped graph with a vertex at the point (-2, 0). When this is adjusted by subtracting 3, the vertex of the V shape is moved down to (-2, -3).
The inequality sign ≥ indicates that we are looking for the region that includes all y-values that are greater than or equal to the function |x + 2| − 3. Therefore, the region of the graph that we are interested in is above this V-shaped graph. The equal part of the inequality ≥ allows us to use a solid boundary line rather than a dashed line, because the points on the graph of y = |x + 2| − 3 are included in the solutions for the inequality.
So, the correct description is a shaded region above a solid boundary line, which represents all the points (x, y) where y is greater than or equal to the value of |x + 2| minus 3.
PLS HELP!
which ordered pair represents point C
The graph of the function f(x)=|x+3| is translated 5 units down.
What is the equation of the transformed function?
a triangular piece of stained glass has an area of 6 square inches and a height of 3 inches. what is the length of the base
The length of the base is 4 inch.
It is required to find the length of the base.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given:
Let b be the length of the base.
h=3 inch.
Area = 6 square inches
a=1/2bh
6=1/2b*3
b=4 inch.
Therefore, the length of the base is 4 inch.
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Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10 each and short-sleeved shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeved shirts that can be purchased?
Alex originally paid $5200 for her car 1 year ago. The value of her car now is $4,420. What is the percent of decrease in the value of her car?
Answer: 15%
Step-by-step explanation:
Given: The original value of car : [tex]\$5,200[/tex]
The value of car after one year : [tex]\$4,420[/tex]
Now, the percent of decrease in the value of her car is given by :-
[tex]\dfrac{\text{Change in price}}{\text{Original price}}\times100\\\\\\=\dfrac{5200-4420}{5200}\times100=15\%[/tex]
Hence, the percent of decrease in the value of her car = 15%
Jane is x years old today. her brother kenny is 4 years older. after seven years their total combined age will be 24 years. write a linear equation for their total combined age after seven years. fine james age today. answer
3 yards of fabric for $13.47
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: Point B is in the interior of \(\angle ADC). Conjecture: ∠ADB≅∠BDC
Answer:
Just because it is in the interior doesn't mean it is on the bisecting line, and ADB could be an obtuse angle
Step-by-step explanation:
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10
Given
The equation in the form
[tex]x^{4}+95x^{2}-500 =0[/tex]
Find the factor of the above equation
To proof
factoring the above equation
we get
[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]
now sloving the equation we get the value
x² = 5
x² = -100
[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]
The factor of the equation is
[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]
Hence proved
In quadrilateral ABCD, diagonals AC and BD bisect one another:
What statement is used to prove that quadrilateral ABCD is a parallelogram?
Angles BAD and ADC are congruent.
Corresponding angles BCD and CDA are supplementary.
Sides CD and DA are congruent.
Triangles BPA and DPC are congruent.
For all pairs of real numbers N and P, where N =5P+ 4, p=? Please help!!!!
A: N/5-4
B: B/5+4
C: 5N-4
D: 5-4/5
the graph below represents y=x. If the slope of the above equation is changed from 1 to 4 which graph best represents the new equation
Answer:
The graph of the new equation is shown in figure 2.
Step-by-step explanation:
Consider the provided function.
[tex]y=x[/tex]
The graph of the above function is shown in figure 1.
The slope intercept form is:
[tex]y=mx+c[/tex]
Where m is the slope and c is the y intercept.
Now, compare the slope intercept form with the provided function.
By the comparison it can be conclude that the slope of the provided function is 1 and y intercept is 0. As the coefficient of x is 1.
We need to change the slope from 1 to 4.
So change the coefficient of x from 1 to 4.
Thus, the required function is [tex]y=4x[/tex]
The graph of the new equation is shown in figure 2.
Eight people compete in a downhill ski race assuming that there are no ties in how many different orders can skiers finish
There are a total of 8! different orders in which a skier can finish the race.
What are Permutations and Combinations?
Objects from a set may be chosen in a variety of ways, usually without replacement, to create subsets. These methods are known as permutations and combinations. When the order of selection is a consideration, this process of choosing subsets is known as a permutation; when it is not, it is known as a combination.
In the given question, we have 8 people, who compete in a downhill ski race.
Also, It is also given that there are no ties in the race.
So, There will be only one person among 8 people, who will rank 1,
Similarly, There will be only one person who will rank 2, and so on till rank 8.
So, The total number of orders a skier can finish the race will be:
Total number of ways = [tex]1 \times 2 \times 3 \times 4 \times 5 \times 6 \times7 \times 8[/tex]
The total number of ways is 8!
Hence, The total number of different orders that a skier can finish will be 8!.
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Find the percent change from 48 to 228. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
There is an increase in percentage from 48 to 228 is 375%.
Given that, the percent change from 48 to 228.
What is the percent change?Percentage change calculator determines the difference in values and the percent change from the original value to the new value.
Here, the difference in values = 228-48 = 180
We know that, percentage increase = Increase ÷ Original Number × 100
Now, 180/48 × 100
= 3.75 × 100
=375%
Therefore, there is an increase in percentage from 48 to 228 is 375%.
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The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
If the Smith's want to use square tiles, which are 6 inch on each side, in the area not covered by the carpet, how many tiles will they need?
Answer:
Correct answer is 768 tiles.
The Smiths would need 768 tiles to cover the area not occupied by the carpet in their 15 ft by 20 ft room.
Explanation:To solve this problem, let's first understand the dimensions. The room is 15 ft by 20 ft which gives a total space of 300 ft2. The carpet is 9 ft by 12 ft, so it will cover an area of 108 ft2.
We subtract the area of the carpet from the total area of the room to find the area that needs to be covered with tiles: 300 ft2 - 108 ft2 = 192 ft2.
Each square tile measures 6 inches by 6 inches. We must convert this to feet, as our other measurements are in feet. So, each tile is 0.5 ft by 0.5 ft, giving an area of 0.25 ft2 per tile.
Finally, we divide the total tile area needed (192 ft2) by the area of each tile (0.25 ft2). This gives us: 192 ÷ 0.25 = 768 tiles.
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You drive 8 miles from your house to your friend's house. Your house is at an elevation of 240 feet. Your friend's house is at an elevation of 680 feet. What is the mean change in elevation per mile?
Which expression is equivalent to −4.7+(−0.3)+(−1.4) ?
A.) (4.7+0.3)+(−1.4)
B.) −4.7−(0.3−1.4)
C.) −4.7+(0.3+1.4)
D.) −(4.7+0.3+1.4)
A mother is 4 times as old as her daughter. in 3 years, the mother will be 3 times as old as her daughter. how many years old is the daughter now?
The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the football’s maximum height? Round to the nearest tenth. yds. How far is the football kicked? yds.
Answer:
Maximum height achieved by football = 25.5 yards.
Distance traveled by football 51 yards.
Step-by-step explanation:
Path of a football kicked by a field goal kicker can be modeled by the equation y = -0.03x² + 1.53x.
Where x represents horizontal distance and y represents height of the football.
For maximum, height we will find the [tex]\frac{dy}{dx}[/tex] ( derivative ) of the equation and equate it to zero.
[tex]\frac{d(y)}{dx}[/tex] = [tex]\frac{d}{dx}[/tex] (-0.03x² + 1.53x )
[tex]\frac{dy}{dx}[/tex] = -0.03 × 2x + 1.53
By putting [tex]\frac{dy}{dx}[/tex] = 0
-0.06x + 1.53 = 0
0.06x = 1.53
x = [tex]\frac{1.53}{0.06}[/tex] = 25.5 yards
Therefore, maximum height achieved by the ball is 25.5 yards.
Now for horizontal distance covered by ball y should be 0
-0.03x² + 1.53x = 0
x ( 1.53 - 0.03x ) = 0
0.03x = 1.53
x = [tex]\frac{1.53}{0.03}[/tex] = 51 yards.
Football was kicked 51 yards.
Factor the expression. 6g^2+11g-35
Answer:
=(3g-5)(2g+7)
Step-by-step explanation:
We have f '(x) = 6x2 + 6x − 432, so f ''(x) = 12x+6 correct: your answer is correct. , which equals 0 when
To find the values of x where f ''(x) equals 0, solve the quadratic equation 12x + 6 = 0 by setting it equal to zero and solving for x: x = -1/2.
Explanation:To find the values of x where f ''(x) equals 0, we need to solve the quadratic equation 12x + 6 = 0. To do this, we set the equation equal to zero and solve for x:
12x + 6 = 0
12x = -6
x = -6/12
Simplifying, we find that x = -1/2.
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What is the sum on 1/9, 2/3, and 5/18?
a. 12/9
b. 19/18
c. 8/30
d. 4/15