Answer: do you need me to answer all or anthor example.
Step-by-step explanation:
I will answer
It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function?
N, = 350,000(0.52)
A.87,500
B.25,591
C.175,000
D.21,875
25,591 cans are still in use after 4 years of recycling and re-using. The solution has been obtained by using functions.
What is a function?
A function is a connection between a set of inputs and one output for each input. The usual notation for a function is f(x), where x represents the input. Usually, a function is written as y = f(x).
We are given a function as N = 350,000 [tex](0.52)^{t}[/tex]
t is given to be 4 years.
Substituting this in the function, we get
⇒N = 350,000 [tex](0.52)^{4}[/tex]
⇒N = 350,000 * 0.07311616
⇒N = 25,590.6
⇒N = 25,591
Hence, 25,591 cans are still in use after 4 years of recycling and re-using.
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Full question has been attached below
Jll company in 2012 had sales of 800,000 in 2022 sales were up 75% . Calculate the sales for 2021.
Answer:
860,000.
Step-by-step explanation:
If the sales in 2022 were up 75% from 800,000, the sales in 2022 would be 800,000 + (800,000 * 75%) = 800,000 + 600,000 = 1,400,000.
To find the sales for 2021, we'll have to use the average annual growth rate to find the sales in between 2012 and 2022.
Let's assume that the sales grew linearly, so the average annual growth rate would be (1,400,000 - 800,000) / (2022 - 2012) = 600,000 / 10 = 60,000.
The sales in 2021 would then be 800,000 + 60,000 = 860,000.
Write an equation for the function graphed
Answer:
y = |x - 3| - 1
Step-by-step explanation:
The vertex of the absolute value function graphed is (3, -1). The formula for absolute value is y = a |x - h| + k, where (h, k) is the vertex. The a stretches the graph, although this graph isn't stretched. So a is 1, which is the same as multiplying by 1. Plugging 3 as h and -1 as k into the formula results in y = |x - 3| - 1.
what is the inequality shown
The inequality on the graph is written as:
-4 < x ≤ 5
What is the inequality shown on the number line?
Here we have an inequality graphed on a number line.
First, we can see that we have an open circle at x = -4 and then the line goes to the right.
That means that the value of x must be larger than -4, so we can start by writting:
-4 < x
Then we have a closed circle at x = 5.
That means that x can be smaller or equal to 5, then:
x ≤ 5
Then the inequality is:
-4 < x ≤ 5
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Consider the expressions {4x^3+2x^2+6x+7}/{2x+1} and 2x^2+3+(4/{2x+1}.)
a) Show that these expressions are equal when x=10.
b) Explain why these expressions are not equal when x=-1/2.
c) Show that these expressions are equal for all x other than-1/2.
In parts (a) and (c), begin by explaining what your strategy for solving will be.
The given expressions {4x^3+2x^2+6x+7}/{2x+1} and 2x^2+3+(4/{2x+1}) are equal at x = 10, they are not equal at x = -1/2, and they are equal for all x other than -1/2.
Substitute x = 10 in the given expressions, we get
{4x^3+2x^2+6x+7}/{2x+1}
= (4000+200+60+7)/21
=203.19
2x^2+3+(4/{2x+1}.)
200+3+4/21
=203.19
Hence, the given expressions are equal when x = 10
Now substitute x = -1/2 in the given expressions
={4x^3+2x^2+6x+7}/{2x+1}
=(4*-1/8+2*1/4+6*-1/2+7)/0
2x^2+3+(4/{2x+1}.)
=2*1/4+3+4/0
When we substitute the value x= -1/2 then it divide by 0 and value will be infinite and hence we can say that the values are not equal at x = -1/2
2x^2+3+(4/{2x+1}.) take LCM
{4x^3+2x^2+6x+7}/{2x+1} here both expression are equal and we can't able find the value at x = -1/2 but for other value of x they are equal.
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What is the circumference of this circle?
Use π = 3.14
6 cm
If the parent function is f(x) = x³, which transformed function is show in the graph?
The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.
What is transformation?
Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.
Translation, rotation, reflection, and dilation are all methods of transformation.
We are given a graph, from which we can say that when x = 3, then y = 0
The function must satisfy these values.
The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).
Also, the translation is 3 units to the right.
So the function shown in the graph is g(x) = (x - 3)³.
Hence, the transformed function is g(x) = (x - 3)³.
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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?
g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3
Factorise: 16x4 - y4
Answer:(4x^2 + y^2)(2x + y)(2x - y)
Step-by-step explanation:
16x^4 - y^4
= (4x2)^2 - (y^2)^2
= (4x^2 +y^2)(4x^2 - y^2)
=(4x^2 + y^2)( (2x)^2 -y^2)
= (4x^2 + y^2)(2x + y)(2x - y).
The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be
used to find the length of the remaining side?
The equation that can be used to find the length of the remaining side is z² = 14² - 9²
How to determine the length of sideUsing the Pythagorean theorem that states that the square of the hypotenuse side is equal or equivalent to the sum of square of the other two sides.
This is represented as;
x² = y² + z²
Given that the parameters are enumerated as;
x is the hypotenuse sidey is the opposite sidez is the adjacent sideNow, substitute the values
14² = 9² + z²
collect like terms
z² = 14² - 9²
Hence, the equation is z² = 14² - 9²
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The length of the remaining side can be calculated using 14² = x² + 9² is 10.7 units
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:
hypotenuse² = adjacent² + opposite²
Let x represent the missing side.
The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Hence:
14² = x² + 9²
x² = 14² - 9²
x² = 115
x = 10.7 units
The length of the remaining side is 10.7 units
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A student moves into a bigger apartment that rents for $750 per month. That rent is $200 less than twice what she had been paying. Find her former
rent in dollars.
Answer:
$475
Step-by-step explanation:
x = former rent
2x - 200 = 750
2x = 750 + 200 = 950
x = 950/2 = 475
Write the equation is slope intercept form given
f(0) = -3 and f(1) = 2
The equation is slope-intercept form is equal to y = 5x - 3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (-3, 2).At point (0, -3), a linear equation of this line can be calculated in slope-intercept form as follows:
y - (-3) = (2 + 3)/(1 - 0)(x - 0)
y + 3 = 5x
y = 5x - 3.
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Which of the following are equivalent to x2 – 4x + 9? Select four answers.
A. (x – 3)2 – 4x
B. (3x2 – 3x + 1) – (2x2 + x – 8)
C. (x – 3)(x + 3) – 2x
D. (x – 3)2 +2x
E. (x – 5)(x + 1) +14
F. (8x2 + 2x) – (4x2 + 6x) + (9 – 3x2)
Answer:
a).2x-6-5x-12x. this is answer
On average the number of drum sets sold in Ohio each year is equivalent to eight times the average number sold yearly in Vermont. If, on average, there are 79,992
drum sets sold each year in Ohio, how many are sold in Vermont?
5.
Jenny had to increase her gas budget from $300 per month to $350 per
month. What is the percentage increase in Jenny's budget?
Answer:
16.66667% increase
Step-by-step explanation:
100 x 350 - 300/ 300 = 50/3 = 16.66667% increase
Formula for percent increase is below↓
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The algebraic equation for the statement is 21 = 2 x - 5
How to write the algebraic equations ?Algebraic equations can be written using mathematical symbols and operations to represent relationships between variables or quantities. Variables are the quantities that the equation is trying to represent or solve for.
There is only one variable here and we can call it x.
The number is doubled so the representation would be :
= 2 x
This is then decreased by 5 and becomes :
= 2 x - 5
This is equated to 21 to become:
21 = 2 x - 5
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What is the result when the number 45 is increased by 57%?
Answer: The result when the number 45 is increased by 57% is approximately 70.65.
Step-by-step explanation:
To find the result when the number 45 is increased by 57%, we need to calculate 45 * (1 + 0.57), where 0.57 represents 57% as a decimal.
Performing the calculation, we get:
45 * (1 + 0.57) = 45 * 1.57 = 70.65
So, the result when the number 45 is increased by 57% is approximately 70.65.
Answer:
70.65
Step-by-step explanation:
The new value =
45 + The value of the percentage increase =
45 + (57% × 45) =
45 + 57% × 45 =
(1 + 57%) × 45 =
(100% + 57%) × 45 =
157% × 45 =
157 ÷ 100 × 45 =
157 × 45 ÷ 100 =
7,065 ÷ 100 =
70.65
The table shows the value of a camper [tex]t[/tex] years after it is purchased. It is an exponential decay function.
a. What is the value of the camper after 5 years? Round to the nearest dollar.
The value of the camper after 5 years is given as follows:
$15,155.2.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.From the table, the rate of change is given as follows:
b = 29600/37000
b = 0.8.
Then the value of the camper after five years can be obtained applying the recursion, multiplying the value after 4 years by the rate of change of 0.8, as follows:
18944 x 0.8 = $15,155.2.
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If one factor of 2 numbers is 2860 is 13,what is the other factor
The factors of numbers let us know that the other factor of 2860 is 220.
Factors of a number.Multiples and factors are connected to one another. The number that divides a given quantity exactly, leaving no residue, is said to be a factor of the quantity.
We may write a × b = c to represent any given integer. c is a multiple of "a" and "b". "a" and "b" are factors of c according to the concept of factors and multiples since c may be divided by both a and b.
Given there are two numbers in which one factor is 13 and the multiple is 2860, then we can write it as:
13 × b = 2860
where;
b = the other factor
b = 2860/13
b = 220
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statement that must be true for the parallelogram is
D. < CAD is congruent to < ACBWhat is alternate internal angles?Alternate internal angles are pairs of angles that lie on opposite sides of a transversal line intersecting two parallel lines. The angles are on the interior (between the two parallel lines) and are not adjacent to each other.
These angles are equal in measure (i.e., they are congruent), which means that if one angle has a certain degree of measure, the other angle will have the same degree of measure.
In the problem, the diagonal of the parallelogram is the transversal line and it is used to make the alternate internal angle theorem possible
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for which values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent
A: No values
B. When d = 0
C: when d = 1
D.All values
Answer: A) No values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent.
What does "equivalent value" mean?They are the same if one amount or value has the same value as another.
We need to set the formulae 12d + 8 and 4(3d + 5) - 8 equal to one another and solve for k to get the values of k for which they are equivalent:
12d + 8 = 4(3d + 5) - 8
When we simplify this equation, we obtain:
12d + 8 = 12d + 12
When we take away 12d from both sides, we obtain:
8 = 12
There are no variables of k for which the expressions are similar because this equation is false for all values of d.
As a result, the response is A) No values.
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What ratios and rates? how can you use ratios and rates to describe quantities and solve problems?
The Ratios, Rate and unit rate are used to solve many real-world problems.
Let us defined ratios, rates and unit rates and see the real world examples below.
As a ratio is a comparison of two numbers or measurements.
For example, if a store sells 5 black color pens and 7 blue color pens, then the ratio of black to blue pens is 5 to 7.
A rate is also a ratio in which the two terms are in different units.
For example, if 2 galloons of milk costs 8 dollar, then the rate is 2galloons for
8 dollar. And the unit is galloons per dollar.
As Rates are used in our daily life, such as when we work 40 hours per week or take 2 liters of water per day. When rates are expressed as a quantity of 1, such as 2 liters of water per day that is, per 1 day or 6 miles per hour that is, per 1 hour. So they can be defined as unit rates.
Hope this helps
Answer:
to describe the same relationship between quantities or to compare two quantities. A rate is a special type of ratio that compares quantities with unlike units. A unit rate compares a quantity of something with a single unit of a different quantity.
Find 4 rational numbers between
OR
-1
6
and
5
Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240
How to Identify Rational Numbers?A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.
First, we have to make the denominators the same.
We multiply 1/5 by 48 and 1/6 by 40 to get:
48/240 and 40/240
Thus, the other rational numbers between them are;
41/240, 42/240, 43/240, 44/240
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Complete question is;
Find four rational numbers between 1/5 and 1/6
For four months, you have saved $25 per month.
You now have $175 in your savings account.
a. Use your result from Exploration 2 to
write an equation that represents the
balance A after t months.
Answer:
A=25t.
Step-by-step explanation:
..........................
The Belmont race track known as "BIg Sandy" is 1.5 miles long. In 1973, Secretariat won the Belomont Stakes race in 2 minutes and 30 seconds. Assuming he ran on "Big Sandy", what was his unit speed in miles per hour
Answer:
Below
Step-by-step explanation:
If he ran ONCE around the track he ran 1.5 miles in 2 .5 minutes
We will need to use a conversion factor of 60 min / 1 hr :
1.5 mi / 2.5 min * 60 min / hr = 1.5 *60 / 2.5 m/hr = 36 m/hr
An office block has five floors (ground, 1, 2, 3 and 4), all connected by a lift. When it goes up
to any floor (except 4), the probability that after it has stopped it will continue to rise is 3/4.
When it goes down to any floor (except the ground floor), the probability that after it has
stopped it will continue to go down is 1/4. The lift stops at any floor it passes.
The lift is currently at the first floor having just descended. Calculate the probability of
these events.
a Its second stop is the third floor.
b Its third stop is the fourth floor.
c Its fourth stop is the first floor.
Answer:
Step-by-step explanation:
a) The second stop is the third floor:
The first stop is the first floor, so the probability of going up from the first floor is 3/4.
The next stop is the third floor, so the probability of going up from the second floor (which is the first floor in this scenario) to the third floor is 3/4.
The probability of both events happening is the product of the individual probabilities: (3/4) * (3/4) = 9/16.
b) The third stop is the fourth floor:
The first stop is the first floor, so the probability of going up from the first floor is 3/4.
The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.
The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.
The probability of all three events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) = 3/16.
c) The fourth stop is the first floor:
The first stop is the first floor, so the probability of going up from the first floor is 3/4.
The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.
The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.
The next stop is the first floor, so the probability of going down from the fourth floor to the first floor is 3/4.
The probability of all four events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) * (3/4) = 9/64.
Kayla and Kevin have the same-size notebooks.
Kayla covered 5/6 of hers with stickers. Kevin covered 5/8 of his with stickers. Who covered more of the notebook? Explain your answer.
Solving provided question, we can say that The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.
What is least common multiple?The least common multiple, or the least common multiple of the two integers a and b, is the smallest positive integer that is divisible by both a and b. LCM stands for Least Common Multiple. Both of the least common multiples of two integers are the least frequent multiple of the first. A multiple of a number is produced by adding an integer to it. As an illustration, the number 10 is a multiple of 5, as it can be divided by 5, 2, and 5, making it a multiple of 5. The lowest common multiple of these integers is 10, which is the smallest positive integer that can be divided by both 5 and 2.
To compare the proportion of each notebook covered with stickers, we need to find a common denominator for the fractions.
The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.
So, Kayla covered more of her notebook with stickers, as 20/24 is greater than 15/24.
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Marissa wants to blend candy selling for $1.50 per pound with candy costing $2.40 per pound to get a mixture that costs her $2.10 per pound to make. She wants to make 18 pounds of the candy blend. How many pounds of each type of candy should she use?
Pounds of $1.50 per pound candy =
Pounds of $2.40 per pound candy
Answer: 6 pounds and 12 pounds.
Step-by-step explanation:
1.5(x)+2.4(18-x)=2.1(18)
1.5x+43.2-2.4x=37.8
1.5x+43.2=37.8+2.4x
0.9x=5.4
x=6 pounds of $1.50 candy
18-6=12 pounds of $2.40 candy
(check my work to see if it's correct :))
what formula is used to determine the percentage change in quantity demanded
Answer:
slope
Step-by-step explanation:
Step-by-step explanation:
always find the quantity of 100%.
then
1% = 100%/100
then calculate the absolute quantity change.
then divide the quantity change by 1% to see how many % fit into it.
and that is your answer.
so, if the original quantity is q1, the new quantity is q2, then the % of quantity change is
|q1 - q2| / (q1/100)
or
100 × |q1 - q2| / q1
where || means the absolute value.
Applying Mathematics in real life context
Informe the coach
Tach
You put two tages in the field. The coordinames for target I (6 Points)
The coordinates for target 2 (4 points). See the figure below.
You asked the players to shoot the ball on the targets 4 times. You added that if
they hit one of the targets, they get the target points
Test 1:
Messi shot the ball. His ball followed the path of the equation where x is the target
points:
1 times
3(3x-4)= 24
6.8 (2.3x + 5.7) = 132.6
Test 2:
Ronaldo shot the ball. His ball followed the path of the equation where y is the
target points:
(6y-18) = 12
8.2 (-5) = -16.4
2 times
2 times
Answer:
Based on the information given, it seems like Messi and Ronaldo were asked to shoot the ball at two targets, target 1 and target 2, and the points they earned would be based on which target they hit.
In Test 1, Messi's first shot followed the equation 3(3x-4) = 24. To determine which target he hit, we need to solve for x. Using algebra, we can simplify the equation to 9x - 12 = 8, and then add 12 to both sides to get 9x = 20. Dividing both sides by 9, we find x = 2.2. Since x represents the number of points earned, this means Messi earned 2.2 points with this shot.
For Messi's second shot, the equation is 6.8 (2.3x + 5.7) = 132.6. To solve for x, we can start by dividing both sides by 6.8 to get 2.3x + 5.7 = 19.5. Subtracting 5.7 from both sides, we find 2.3x = 13.8. Dividing both sides by 2.3, we find x = 6.
In Test 2, Ronaldo's first shot followed the equation (6y-18) = 12. To solve for y, we can add 18 to both sides to get 6y = 30, and then divide both sides by 6 to get y = 5. This means Ronaldo earned 5 points with this shot.
For Ronaldo's second shot, the equation is 8.2 (-5) = -16.4. To solve for y, we need to determine the value of x. Since the equation is just a constant times a negative number, we can simplify it to 8.2 * -5 = -41. This means Ronaldo earned -41 points with this shot.
It's important to note that negative points are not possible in this scenario, as the targets only have positive point values.
Step-by-step explanation:
Leyan bought 2 3/4 pounds of apples for $1.32 per pound, 1 1/2 pounds of peaches for $1.20 per pound, and some tomatoes, all from a grocery store. The total cost of his purchase was $9.63.
How much money did Leyan spend on tomatoes?