Using the linear function given, the tree will have a height of 5.25 feet in 3 years
What is Linear FunctionLinear functions are mathematical functions where the output values are in direct proportion to the input values. A linear function has the form
y = mx + c, where m is the slope of the line and c is the y-intercept.
In this problem, the function given already models y = mx + c
Since y = 3/4x + 3;
The height of the tree in 3 years can be solved as;
y = 3/4(3) + 3
y = 9/4 + 3
y = 5.25
The height of the tree in 3 years is 5.25 feet
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The first laptop ever was sold was the Osborne 1. It came onto the market in 1981, and
it had a mass of 11 kg. Suppose that since 1981 the mass of laptops has decreased at an
average rate of 4. 7% per year. What was the approximate weight of a laptop in 2019?
The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.
1981: 11 kg
1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)
1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)
1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)
2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)
The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.
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What is the area of equilateral ∆ having side 12 cm?
Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
Describe the triangle.In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.
Here,
Given : side = 12cm
Area of an equilateral triangle
=> √3/4 * side²
Side of triangle =12 cm
Area of an equilateral triangle
= > √3/4 * 12²
=>√3/4 * 12*12
=> 62.28 cm²
Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
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Charlie and Susan are planning a part for 10 people. Charlie finds a location that charges a initial fee of $20 plus $25 per person. Susan finds a location whose rental fee is represented by the equation y=15x+100, where x is the number of people in attendance and y is the total cost. Select all the statements that are true. A. Charlie's location is a cheaper location B. Susan's location is cheaper for 10 people. C. The charge for each additional person is greater for Susan's location. D. The charge for each additional person is greater for Charlie's location. E. If the number of people at the party changes to 12, the total cost at each location is the same. There are TWO answers
Please help my promotion is coming No links I just need the answers
Answer:
B. Susan's location is cheaper for 10 people.
D. The charge for each additional person is greater for Charlie's location.
[tex] \frac{3}{5} \times \frac{55}{100} [/tex]
Answer:
Hello There!!
Step-by-step explanation:
The answer is: 33/100.You time the numerator by the numerator and the denominator by the denominator and simplify it which is 33/100.
hope this helps,have a great day!!
~Pinky~
Step-by-step explanation:
I hope it helps you have a great weekend
Find the sum of the first 44 terms of the following series, to the nearest integer.
5,12, 19,...
Answer:6842
Step-by-step explanation:
13684/2
What are the 3 linear equations?
The 3 linear equations are
1. y = mx + b
2. ax + by = c
3. x/a + y/b = 1
1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.
2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.
3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.
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-2(11-12x) = -4(1-6x)
Answer:
0=18
Step-by-step explanation:
not simplified.
Answer:
There is no answer.
Step-by-step explanation:
-2(11 - 12x) = -4(1-6x)
First you need to simplify the equation, using distributive property.
Distribute -2 to the numbers within the parentheses.
-2*11 = -22
-2*-12x =24x
= 24x - 22
Then distribute -4 among 1 and -6.
-4*1 =-4
-4*-6x = +24x
= 24x - 4
And because
24x - 22 does NOT equal 24x - 4
There is no answer because they are not equivalent, making the equation itself false/untrue.
What is the measure of ZB?
Answer:
m<B=60°
Step-by-step explanation:
an exterior angles equals the sum of its two remote interior angles, so:
m<A+m<B=m<BCG:
3x+4x=10x-45
7x=10x-45
-3x=-45
x=15
to find the measure of <B:
since m<B=4x:
4(15)=60°
so, m<B=60°
Answer:
Step-by-step explanation:
When working modulo m, the notation a^-1 is used to denote the residue b for whichab = 1 (mod m), if any exists. For how many integers a satisfying 0 < a < 100 is it true thata(a − 1)−¹ = 4a-¹ (mod 20)?Please hurry up guys!!
There are 10 integers that satisfy 0 < a < 100.
What are integers?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.
We have to find integers that satisfy 0 < a < 100.
a(a − 1)⁻¹ ≡ 4a⁻¹ (mod 20)
a ≡ 4a⁻¹(a − 1)(mod 20)
a² ≡ 4(a-1)(mod 20)
a² - 4a + 4 ≡ 0(mod 20)
(a - 2)² ≡ 0(mod 20)
a = 2 + 10n | for n = (0, 1, 2, 3.....9)
Hence, there are 10 integers that satisfy 0 < a < 100.
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Type the correct answer in the box. Round your answer to the nearest tenth. The population of Cuba is 1.3 million. The country's population is expected to grow at a rate of 4% each year. The population of Cuba will be million in 10 years.
The population of Cuba in 10 years will be 1.9243 million.
What is meant by exponential growth?A process called exponential growth sees a rise in quantity over time. It happens when a quantity changes at an instantaneous rate that is proportionate to the quantity itself with respect to time.
Data patterns that exhibit exponential growth exhibit quicker rate of expansion over time. Compounding produces exponential returns in the financial world. Savings accounts with a compound interest rate have the potential to expand exponentially.
The population growth will be modeled using exponential growth:
f(x) = a(b[tex])^t[/tex]
where:
a be the initial value
b be the growth rate
Substitute the values in the above equation, we get
f(x) = 1.3(1.04[tex])^t[/tex]
The population after 10 years will be:
f(x) = 1.3(1.04[tex])^{10[/tex]
simplifying the equation, we get
f(x) = 1.9243
Therefore, the population in 10 years will be 1.9243 million.
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The population of Cuba in 10 years will be 1.9243 million, if the population is expected to grow at a rate of 4% each year.
What is meant by exponential growth?Quantities increase over time through a process known as exponential growth. It occurs when a quantity shifts at a pace that is proportional to the quantity's own rate of change with regard to time.
Data patterns that show exponential growth expand more quickly over time. In the world of finance, compounding generates exponential profits. Compound interest savings accounts have the potential to grow tremendously.
The population growth will be modeled using exponential growth:
f(x) = a(b)[tex]^{t}[/tex]
where:
a be the initial value
b be the growth rate
Substitute the values in the above equation, we get
f(x) = 1.3(1.04
The population after 10 years will be:
f(x) = 1.3(1.04
simplifying the equation, we get
f(x) = 1.9243
Therefore, the population in 10 years will be 1.9243 million.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
Step-by-step explanation:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
f(–10) = (–10)^2 – 5(–10) + 12 = 100 – (–50) + 12 = 162
The statement "The graph of the function is a parabola" is true. Because the equation of the function is of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0, the graph of the function is a parabola.
The statement "The graph of the function opens down." is true. The coefficient of x^2 is a positive value, which means the parabola opens down.
So, the true statements are
The graph of the function is a parabola.
The graph of the function opens down.
The graph does not contain the point (20, –8)
how to solve -6/ 2/3 (use inverse operations to solve it) please explain!
1. Are the triangles shown below similar? Explain.
Answer:
Step-by-step explanation:
These are the tests for similar triangles:
AA - if 2 pairs of corresponding angles are equal.
SSS - if corresponding sides have the same ratio.
SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.
This diagram does not indicate any of these relationships exist.
Therefore the triangles are not similar.
Find the area of the surface obtained by rotating the circle
x2 + y2 = r 2
about the line
y = r.
The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
To find the area of the surface obtained by rotating the circle
[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.
The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.
When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.
Consider a small strip on the circle at a distance y from the line y = r.
This small strip is at a distance r - y from the y-axis.
The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).
The width of this strip is the change in x, which we can denote as dx.
The area of this small strip is then given by the product of its length and width, which is 2πy dx.
Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):
Total Surface Area = ∫[from -r to r] 2πy dx
Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]
y = ±√(r² - x²)
Since we are considering the upper half of the circle, we take the positive square root:
y = √(r² - x²)
Now, we can rewrite the integral with respect to x:
Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx
To solve this integral, we can make a trigonometric substitution:
Let x = r sin(θ), then dx = r cos(θ) dθ.
When x = -r, θ = -π/2, and when x = r, θ = π/2.
Now the integral becomes:
Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ
Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ
Now, we can use the trigonometric identity:
sin²(θ) + cos²(θ) = 1
√(1 - sin²(θ)) = cos(θ)
Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ
Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2
Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ
Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]
Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]
Since sin(π) = 0 and sin(-π) = 0:
Total Surface Area = 2πr² [(π/2 - (-π/2))/4]
Total Surface Area = 2πr² (π/2)
Total Surface Area = π²r²
So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
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All 210 students in a school went roller skating, to a water park, or both. The number of students who went only to the water park is four times the number of students who went only roller skating. The number of students who went only to the water park is two times the number of students who did both. How many students did both?
60 students out of 210 in a school went both roller skating and water park.
What is algebraic equation ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Have given ,
Total students = 210
Let x = The number of students who went only to the roller skating
and y = The number of students who went to the water park and roller skating
x + 4x + y = 210 ⇒ 5x + y = 210 ......(i)
x + y + 2y = 210 ⇒ x + 3y = 210 ⇒ x = 210 - 3y
Put the value of x in equation no. (i),
5(210 - 3y) + y = 210 ⇒ 1050 - 14y = 210 ⇒ 14y = 1050 - 210
14y = 840 ⇒ y = 60
Hence , 60 students out of 210 in a school went both roller skating and water park.
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One yard of ribbon is 3.5 dollars. How much should one pay for
5/8 yards
Answer:
38
Step-by-step explanation:
One should pay 2.1875 dollars.
What are arithmetic operations?Addition, subtraction, multiplication, and division are the most fundamental operations in arithmetic. However, arithmetic also includes more complex operations like manipulating percentages, square roots, exponentiation, logarithmic functions, and even trigonometric functions, which are analogous to logarithms. It is necessary to evaluate arithmetic expressions in accordance with the intended order of operations.
Given one yard of ribbon is 3.5 dollars
1y = 3.5
where y = yards
dollar for 5/8 yards is
1y x 5/8 = 3.5 x 5/8
5/8y = 2.1875
Hence one should pay 2.1875 dollars for 5/8 yards.
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ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
b 41cm, 40cm, 9cm form a right angle
A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150 of the adults who were parents and 40 of the adults who err not parent’s thought the park should be expanded.
Answer: In this exercise we have to calculate the values of the people who voted to expand the parking lot, so we have to:
Yes: parents will be 150 and not parents 40
No; parents will be 40 and not parents 30
As it is about sets, we have to use the data that were:
total: 250 adults
180 of whom were parents a park should be expanded.
40 of the adults who were not parents thought the park should be expanded.
then calculate that:
Step-by-step explanation:
The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
The two-way table shown in the table is attached below.
What is two way table?
Two-way table is a way of representing of data to better understand it.
Given information-
The total number of adults took the survey is 250.
Total number of parents took the survey is 180.
150 of the adults with children and 40 of those without thought the park should be expanded.
Suppose the number of adults who are not the parents and took the survey is .
As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,
Suppose the parents who does not thing that the park should be expanded is .
There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,
Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.
Hence the two way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
the two way
YES NO
30
30
(parents 150
not parents_40
How many square feet of outdoor carpet will
we need for this hole?
Answer:
8
Step-by-step explanation:
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a
30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
0
1
2
W = # of walleye
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.
As given in the question,
Let 'W' is the random variable represents the number of walleye.
'P(W)' represents its probability
The values are given as follow:
W : 0 1 2
P(W) : 0.09 0.42 0.49
Mean of the walleye 'W' is given by :
= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)
= ( 0 × 0.09 ) + ( 1 × 0.42 ) + ( 2 × 0.49 )
= 0 + 0.42 + 0.98
= 1.4
Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.
The above question is incomplete , the complete question is :
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
W : 0 1 2
P(W) : 0.09 0.42 0.49
Calculate the mean of W.
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Help ill Give brainliest
Answer:
a. 4^12
b. 6^7
c. 8^5
d. 7^2
Step-by-step explanation:
hope this helps :)
How do you identify the solutions in solving linear inequalities in two variables *?
To identify the solutions in solving linear inequalities in two variables, you can first graph the equation on a coordinate plane. Then, you can use the boundary line to identify which regions of the plane satisfy the inequality.
Any points in the shaded regions will be solutions to the inequality. Additionally, you can use the boundary line to identify the points that are not solutions by finding the points that lie on the boundary line.
Example:
x + 2y ≥ 4
The graph of this inequality is a line with a slope of -2/1 and a y-intercept of 4/2. The line will be shaded on the side of the line containing the greater values, which in this case is the side containing the origin.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in the simplest form 12,7,2,...
Answer: common difference = -5
Step-by-step explanation:
This is an arithmetic progression. The common difference will be gotten by subtracting the 1st term from the 2nd term. This will be:
1st term = 12
2nd term = 7
3rd term = 2
Common difference = 7 - 12 or 2 - 7 = -5
It isn't an geometric progression as the ratio isn't thesame
= 2nd term / 1st term
= 7/12
= 3rd term / 2nd term
= 2/7
Therefore, it's an arithmetic progression with difference of -5
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answer:
The area of this parallelogram is 140 square feet.
Step-by-step explanation:
A = bh
A = 14 * 10
A = 140
Hope this helps; have a wonderful day!
Someone help me what’s the answer pls
Chapter 3 Lesson 4 Arithmetic Sequence
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
What is Arithmatic Sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.
The equation to determine the nth term in an arithmetic series
The formula for calculating the sum of an arithmetic sequence's first n terms
There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
Option 1, 4 and 6 are in Arithmatic Sequence as
In 1:
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
again in 4 :
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
and in 6
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
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WHAT IS 2+2=?
giving brainiest for first to answer
Answer:
2+2its4
hope it helps......
What are the solutions of the quadratic equation 2x^2 5x 12 0?
The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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Carmen swam 2 1/3 laps in 3 1/2 minutes. Assume she swam the entire time at the same rate. What was her speed in laps per minute
Raina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges and allows unlimited mileage. Company B has an initial fee of and charges an additional for every mile driven. For what mileages will Company A charge less than Company B
For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.
For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.
For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:
Total cost = initial fee + (mileage * additional cost per mile)
For Company B, this would be:
Total cost = $30 + (mileage * $0.50)
To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:
$50 <= $30 + (mileage * $0.50)
To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:
$20 <= (mileage * $0.50)
Then, we can divide both sides by $0.50:
40 <= mileage
So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
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