The two variables in a scatter plot are called the x-variable or independent variable and the y-variable or also called dependent variable.
The x-variable is typically plotted along the horizontal axis, and the y-variable is typically plotted along the vertical axis. The x-variable is the variable that is being used to explain or predict changes in the y-variable. In other words, it is the variable that is being manipulated or changed to observe changes in the y-variable.
For example, if the x-variable is a person’s age and the y-variable is their income, then the x-variable is the variable that is being changed (age) to observe changes in the y-variable (income). Scatter plots are useful for visualizing the relationship between two variables and can be used to identify correlations, outliers, and trends.
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a researcher recorded information about the possible speeds of a jackrabbit, a gray fox, and a squirrel. the gray fox’s speed is 35 mph
1. The jackrabbit runs at a constant rate, as the rate between the output and the input for each point on the table is constant.
2. The squirrel runs at a constant rate, as the graph is that of a linear function with a constant slope.
3. The rate of the jackrabbit is of 44 miles per hour.
4. The rate of the squirrel is of 11 miles per hour.
5. A.
The gray fox ran at a rate of 35 miles per hour.The squirrel ran slower than the gray fox.The jackrabbit ran faster than the gray fox.B. The jackrabbit ran the fastest.
6. In three hours, the fastest animal will have run 99 miles further than the slowest animal.
7. The point (0,0) means that all the animals, the jackrabbit, the gray fox and the squirrel start from the origin.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
The rates for the jackrabbit are given as follows:
k = 22/0.5 = 44/1 = 44 miles per hour.
This is also equals to k = 0/0, which can assume any value, and the point (0,0) means that all the animals, the jackrabbit, the gray fox and the squirrel start from the origin.
The rate for the squirrel is given as follows:
k = 11/1 = 11 miles per hour.
(as the graph passes through point (1, 11)).
The difference between the rates of the fastest and of the slowest animal is given as follows:
44 - 11 = 33 miles per hour.
Hence in three hours, the distance is given as follows:
3 x 33 = 99 miles.
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What is the slope of the line?
-1/4 is the slope of the line draw in the graph.
What is the slope?An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.
Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.
Slope = (y₂ - y₁) / (x₂ - x₁)
Here, (x₁, y₁) = (4,0)
(x₂, y₂) = (0,1)
Thus, slope = (1 - 0) / (0 - 4)
slope = - 1/4
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Mandy bought p notebooks for the first day of school. She gave her brother 4 of the notebooks. Mandy had more than 3 notebooks left. Which inequality represents p, the number of notebooks Mandy bought?
Answer: 8 or more, There is no exact number.
Step-by-step explanation:
4 - p = -4
then to get to greater than 3, you have to do -4 + 8 = 4
So Mandy bought 8 or more notebooks
4. Mary bought 12 pounds of blueberries to make 5 pies. She divided the blueberries evenly. How many pounds of blueberries were in each pie?
Answer:
2.4
Step-by-step explanation:
12 divided by 5
In order to get it
Answer:
2.4 lbs
also 2lbs 6oz (rounded to the nearest ounce)
Step-by-step explanation:
We are comparing pounds of blueberries to pies.
pounds/pies
= 12pounds/5pies
= 12/5
= 2.4 pounds per pie
Mary used 2.4lbs of blueberries in each pie.
If you need to know the ounces, the .4 part of the 2.4 answer is the ounces. (2 is pounds, .4 is parts of a pound)
There are 16 ounces in a pound.
.4 × 16
= 6.4
2.4 pounds is 2pounds6ounces (rounded to the nearest ounce)
What is the factored form of 3x 24y?
The factored form of the expression [tex]3x+24y[/tex] can be written by using distributive Property as [tex]3(x+8y)[/tex] .
The expression is given as : [tex]3x+24y[/tex] ;
we have to write the factored form this expression ;
we use the distributive property , to write the factored form ,
the distributive property ⇒ states that for any three numbers the condition [tex]a(b+c) = ab+ac[/tex] is satisfied;
the first term of the expression is 3x ,
the second term of the expression is 24y , which can be written as [tex]3\times 8y[/tex] ;
In the first and second term , we can see that 3 is the common factor in both the terms ,
Therefore , the factored form can be written as [tex]3(x+8y)[/tex] .
The given question is incomplete , the complete question is
What is the factored form of the expression [tex]3x+24y[/tex] ?
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After taking the common, the factored form of 3x + 24y is 3(x + 8y).
In the given question, we have to find the factored form of 3x + 24y.
The given expression is 3x + 24y.
The following is how we factor the GCF out of a polynomial:
(1) Determine the polynomial's GCF for each term.
(2) Present each term as the GCF and another factor's product.
(3) To factor out the GCF, use the distributive property.
To solve this question, we take common the number that are common in both terms. Then We solve this expression.
Taking 3 common
3x + 24y = 3(x + 8y)
Hence, the factored form of 3x + 24y is 3(x + 8y).
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The complete answer is:
What is the factored form of 3x + 24y?
Factor this expression completely, then place the factors in the proper location on the grid. X 3 - 1.
The expression will be (x - 1) (x² + x + 1).
How to find the expression ?
As per given x³ - 1, The first things you have to do is rewrite the the expression as :
a³ ± b³ : x³ - 1³
then factorize both expression
a³ ± b³ : x³ - 1³ = (a ± b) (a² ± ab + b²) : (x - 1) (x² + x + 1²)
last, calculate the power of (x - 1) (x² + x + 1²)
(x - 1) (x² + x + 1²) = (x - 1) (x² + x + 1)
Hence, the answer of that question will be (x - 1) (x² + x + 1)
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The set $S$ is the union of the set of all points inside a regular nonagon with side length $2$ units and the set of all points less than $1$ unit away from an arbitrary point on the perimeter of the nonagon. What, in units, is the perimeter of $S$
The perimeter of nonagon in units is 24.28 units.
The perimeter is comprised of 9 segments of length 2 plus the circumference of a circle with a radius of 1 [each curved part of S is 1/9 of this circumference and there are 9 of them ]
The perimeter = 9*2 + 2pi (1) = 18 + 2pi ≈ 24.28 units
Calculate the perimeter of many forms by summing the lengths of their sides. Since there are two of each side length, the perimeter is calculated by simply adding the length and width and multiplying the result by two. The formula for perimeter is perimeter=(length+width)2.
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When renting a limo for prom, the number of people is inversely proportional to the cost per person. Originally there were 3 people and the cost per person was $72. If the number of people changed to 12, what would be the new cost per person?
If the number of people changed to 12, the new cost per person is equal to $18.
What is an inverse variation?In Mathematics, an inverse variation can be modeled or represented by this mathematical expression:
p ∝ 1/c
p = k/c
Where:
p represents the number of people.c represents the cost per person.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
k = pc
k = 3(72)
k = 216
Now, we can determine the value of c:
c = k/p
c = 216/12
c = $18.
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Adaptive Cruise Control with Cloud Connectivity Objective Use MATLA to develop and implement an adaptive cruise control system for vehicles that automatically adjusts the speed to maintain a safe distance from vehicles ahead. The speed information has to be uploaded on the cloud to support connected vehicles and intelligent transport. Hardware Arduino uno x 1, button x 5, distance sensor x 1, 4 digit 7-segment anode display x 1 Description Implement an adaptive cruise control system using the Arduino UNO board. The system is controlled by five buttons of (1) Set_speed, (2) Adaptive_speed, (3) Cancel, (4) Increase_speed, and (5) Decrease_speed. After power on, the display has to show the initial speed of 0. 1. When the increase_speed button is pressed, the speed increases, and when the Decrease_speed button is pressed the speed decreases however without pressing the Set_speed button the speed will not remain constant and it changes slowly over time. 2. When the Set_speed button is pressed the system enters the cruise control mode where the speed is held constant. In this mode, the Increase_speed button and the Decrease_speed button are still functional and can be used to change the Set_speed. If the Cancel button is pressed, the system quits the cruise control mode where the speed decreases slowly. 3. If the Adaptive_speed button is pressed, the speed is set and held constant until a vehicle shows up at the front or an object is detected where the speed automatically decreases. When the road becomes clear, the speed increases to reach the set speed again. In the adaptive cruise control mode, the display has to blink to differentiate this mode from the cruise mode. In this mode, the Increase_speed button and the Decrease_speed button do not function but the Cancel button can still be used to quit the adaptive cruise mode. If the Cancel button is pressed, the display stops blinking and the vehicle speed begins to slow down. 4. The implemented system has to be able to communicate with the ThingSpeak platform to store the speed data on the cloud. ThingSpeak is an Internet of Things (IoT) application that supports MATLAB to analyze and visualize data
The objective is to develop and implement an adaptive cruise control system for vehicles using MATLAB, Arduino UNO, and ThingSpeak that automatically adjusts the speed to maintain a safe distance from vehicles ahead and uploads speed information to the cloud for connected vehicles and intelligent transport.
The system uses an Arduino UNO board, five buttons, a distance sensor, and a 4-digit 7-segment anode display. The buttons include Set_speed, Adaptive_speed, Cancel, Increase_speed, and Decrease_speed. The system has two modes, cruise control, and adaptive cruise control.
In cruise control, the speed is held constant and can be adjusted with the Increase_speed and Decrease_speed buttons. In adaptive cruise control, the speed automatically adjusts to maintain a safe distance from vehicles or objects in front and the display blinks to indicate this mode.
The system also communicates with the ThingSpeak platform to store speed data on the cloud for analysis and visualization in MATLAB.
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Priya was busy studying this week and ran 9 fewer miles than last week. Elena ran as far 1 9 as Priya did this week. Elena only ran 4 miles this week. How many miles did Priya run last week?
Answer:
1) The number of miles Priya ran last week was 43 miles
2) The way Elena found Priya's miles is faster compared to the way it was found here
Step-by-step explanation:
1) The number of miles Priya ran this week = The number of miles Priya ran last week - 7
The number of miles Priya ran this week = 9 × The number of miles Elena ran this week
The number of miles Elena ran this week = 4 miles
Therefore;
Let the number of miles Priya ran last week = x miles
The number of miles Priya ran this week = (x - 7) miles
Therefore, we have
(x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles
x = (36 + 7) miles = 43 miles
The number of miles Priya ran last week = x miles = 43 miles
The number of miles Priya ran last week = 43 miles
2) From (x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles, we have;
(x - 7) = 9 × 4
1/9(x - 7) = 4
Therefore, multiplying by 9, we have;
9 × 1/9(x - 7) = 9 × 4
(x - 7) = 9 × 4 = 36
x - 7 + 7 = 36 + 7
x = 43 miles
Therefore, the way Elena found Priya's miles is faster compared to the way it is found here
Solve for X, Leave in simplest radical form. (Help, and the degree shown is 30)
The simplest radical form of X of the triangle is [tex]\sqrt{}[/tex]30.
How can the value of x be determined in its simplest radical form?AI Recommended Response Division by the radical sign yields the value of x in its simplest radical form.
Due to the absence of any perfect square factors for the number beneath the square root,[tex]\sqrt{}[/tex] 30 is in its simplest radical form.
Due to the fact that the number under the square root,
[tex]\sqrt{}[/tex]30 = [tex]\sqrt{2} * \sqrt{3} *\sqrt{5}[/tex]
may be factored to equal, and that [tex]\sqrt{}[/tex]30 is a perfect square since
is not in its simplest radical form.
so we can add [tex]\sqrt{30}[/tex]
The simplest radical form of X of the triangle is [tex]\sqrt{}[/tex]30
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Which action is most helpful in preventing sexual involvement?
1. bringing condoms “just in case”
2. voicing personal boundaries
3. indicating that parents will be upset
4. suggesting that it is not the right time for a dating relationship
The correct answer for preventing sexual involvement would be option 2: voicing personal boundaries.
Voicing personal boundaries: This action is crucial in preventing sexual involvement.
By clearly communicating one's personal boundaries, desires, and limits, individuals establish their autonomy and expectations within a relationship. Open and honest communication allows both parties to understand and respect each other's boundaries, leading to a healthier dynamic.
Voicing personal boundaries is essential because it allows individuals to communicate their limits and expectations regarding sexual involvement, promoting consent and healthy relationships.
It empowers individuals to take ownership of their bodies and decisions, fostering an environment where all parties involved can make informed choices and respect each other's boundaries.
Hence the correct option is 2.
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A cube and sphere that has same volume
Answer: If a sphere and a cube have the same volume then the ratio of the surface of the sphere to that of the cube is 6: π
Combine as indicated by the signs.
(2x) / (y^(2)-x^(2))- (x)/(y-x)
The expression can be combined as [2x - xy - x²] / [y²-x²]
How to combine the expression as indicated by the signs?An expression is the collection of numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given: 2x/(y²-x²) - x/(y-x)
2x/(y²-x²) + x/(y-x) = 2x/(y-x)(y+x) - x/(y-x)
The LCM of (y-x)(y+x) and (y-x) is (y-x)(y+x)
= 2x/(y-x)(y+x) - x/(y-x)
= [2x - x(y+x)] / [(y-x)(y+x)]
= [2x - xy - x²] / [(y-x)(y+x)]
= [2x - xy - x²] / [y²-x²]
Note: y²- x² = (y-x)(y+x)
Thus, the expression can be combined as [2x - xy - x²] / [y²-x²]
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DOES ANYONE KNOW THE ANSWER or know if 2 to the square root of 3 divided by b is right?
Step-by-step explanation:
you did not say what needs to be done.
simplify ?
sqrt(12/b²)
12 = 4×3
4 is a square number (2² = 4).
3 is not.
b² is per definition a square "number".
in a multiplication or division we can apply the square root (or any root) individually to the different factors involved.
so,
sqrt(12/b²) = sqrt(12)/sqrt(b²) = sqrt(4×3)/b =
= 2×sqrt(3)/b
FYI - about your question : if somebody does not know (how to get) the answer, he/she will also not be able to doubtlessly determine, if a specific answer is right ...
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
The statements are always true regarding the diagram, as follows:
1. m∠5 + m∠6 = 180°
2. ∠ 2+ ∠ 3 = ∠ 6
3. m∠2 + m∠3 + m∠5 = 180°
What is the interior Angle?An interior angle is defined as an angle produced on the inside of a polygon by extending the sides of the polygon.
Consider Δ ABC with Exterior angles as
∠ 1 , ∠ 4 , and ∠ 6
For Exterior ∠ 1 we have
∠ 1 = ∠ 5 + ∠ 3
This true due to Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 4 we have
∠ 4 = ∠ 5 + ∠ 2.
This true due to the Exterior angle Property of the Triangle
Similarly,
For Exterior ∠ 6 we have
∠ 6 = ∠ 2 + ∠ 3
In a triangle sum of the measures of angles is equal to 180°
∴ m∠2 + m∠3 + m∠5 = 180°
This is true due to Triangle Sum Property
A straight angle has a measurement of 180 degrees, hence a linear pair of angles must sum up to 180 degrees.
∴ m∠5 + m∠6 = 180°
This true due to the Linear Pair.
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Which point is located on the y-axis?
0,-3
-3,0
-3,3
3,-3
Answer:
(0, - 3 )
Step-by-step explanation:
Any point on the y- axis has an x- coordinate of zero
the only point with an x- coordinate of zero is (0, - 3 )
Please help with all of these questions
1. solve 2 x 5/8 leave your answer as a improper fraction a. 7/16 b. 10/16 c. 7/8 d. 10/8
2. solve 9 x 2/3 leave your answer as a improper fraction a. 11/27 b. 18/27 c. 11/3 d. 18/3
3. solve 5 x 3/4 leave your answer as a improper fraction a. 15/20 b. 12/5 c. 15/4 d. 8/2
The solution for each operation, involving multiplication of fractions, is given as follows:
1. 2 x 5/8 = 10/8. (option d).
2. 9 x 2/3 = 18/3. (option d).
3. 5 x 3/4 = 15/4. (option c).
How to multiply fractions?A fraction has the notation given as follows:
Fraction = x/y.
In which the technical terms of each term are given as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.To multiply two fractions, we simply multiply the numerators among themselves, and the denominators among themselves, and then the product of the fractions is given by the multiplication of the numerators divided by the multiplication of the denominators.
For example:
2 x 5/8 = (2 x 5)/(1 x 8) = 10/8.
(as an integer term can be represented by a fraction with denominator one).
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Mariana and her children went into a movie theater and she bought $51.25 worth of
candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She
bought a total of 13 candies and pretzels altogether. Write a system of equations that
could be used to determine the number of candies and the number of pretzels that
Mariana Bought. Define the variables that you use to write the system.
On solving the provided question, we can say that - by the help of unitary method we have total cost is 4.74* 13 + 3.25 = $64.87
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
he bought = $51.25 worth of candies and pretzels
ach candy costs = $4.75 and each pretzel costs = $3.25.
total cost is 4.74* 13 + 3.25 = $64.87
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Calculate the double integral.∫∫R 8x/1+xydA ; R = [0,8]×[0,1]
The double integral ∫∫R 8x/1+xydA ; R = [0,8]×[0,1] is evaluated using the iterated integral formula, and the value of the integral is found to be 5.99146454710798.
The double integral can be calculated using the iterated integral formula:
∫∫R 8x/1+xydA = ∫0,1 ∫0,8 8x/1+xydxdy
= ∫0,1 [8x/1+xydx]|0,8dy
= ∫0,1 [8ln(1+8y) - 8ln(1+0)]dy
= 8ln(1+8) - 8ln(1)
= 8ln(9) - 8ln(1)
= 8ln(9)
= 5.99146454710798
The double integral is calculated by transforming it into an iterated integral. This is done by evaluating the inner integral first and then the outer integral. The inner integral is evaluated by using the fundamental theorem of calculus and the outer integral is evaluated by substituting the upper and lower limits of the integral. Finally, the value of the double integral is calculated by subtracting the expression for the lower limit from the expression for the upper limit.
The double integral ∫∫R 8x/1+xydA ; R = [0,8]×[0,1] is evaluated using the iterated integral formula, and the value of the integral is found to be 5.99146454710798.
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Which of the following statements are true when considered direct student loans
(Stafford Loans)?
A direct subsidized loan requires you start paying interest immediately while you
are in school.
A direct unsubsidized loan will not cover interest while you are in school, and
you are responsible for paying the interest while you are in school.
A direct subsidized loan will cover the interest on the loan while you are in
school.
A direct unsubsidized loan will not require interest be paid until you graduate or
leave the school.
You are responsible for paying the interest while you are in school because a direct unsubsidized loan does not cover it.
What is meant by direct student loans?The Federal Direct Loan Program through William D. Ford offers "loans with low interest rates that parents and students can use to help cover the expense of a student's post-high school education. A bank or other financial institution is not the lender; rather, it is the U.S. Department of Education."
The U.S. Department of Education issues federal direct loans, which are loans for students. In most cases, if you obtained a federal student loan or consolidated your debt on or after July 1, 2010, you have a federal Direct Loan.
Federal and private loans are the two main categories of student loans. Federal government funding is used to support federal parent and student loans. Private student loans are made by lenders such as banks, credit unions, state agencies, or educational institutions and are not provided by the federal government.
Therefore, the correct answer is option a) A direct unsubsidized loan will not cover interest while you are in school, and you are responsible for paying the interest while you are in school.
The complete question is:
Which of the following statements are true when considered direct student loans (Stafford Loans)?
A direct subsidized loan requires you start paying interest immediately while you are in school.
A direct subsidized loan will cover the interest on the loan while you are in school.
A direct unsubsidized loan will not require interest be paid until you graduate or leave the school.
A direct unsubsidized loan will not cover interest while you are in school, and you are responsible for paying the interest while you are in school.
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Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown.
Each section will be a different color, so they need to know the area of each section.
1. Write an expression for the total area of the wall. Explain how you came up with your expression. (3 points)
2. To find the area of each section, what do you need to do to the total area? (3 points)
3. Write an expression for the area of each section of the wall. (4 points)
5(10x) is the expression for the total area of the wall, the total area you just need to divide by five to find the area of each section and 10x is an expression for the area of each section
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Todd and his friends are painting 5 equal sections of a wall.
The wall is 10 feet tall, but its length is unknown.
Let the unknown length is x
Expression for the total area of the wall is 5(10x)
To get area you do like the times width so it’s 10 times X and theres five sections
If you have the total area you just need to divide by five to find the area of each section
10x is an expression for the area of each section of the wall because it’s just the length times the width of the wall segment
Hence, 5(10x) is the expression for the total area of the wall, the total area you just need to divide by five to find the area of each section and 10x is an expression for the area of each section
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Timmy writes the equation f(x) = f(x) equals StartFraction one-fourth EndFraction x minus 1.x – 1. He then doubles both of the terms on the right side to create the equation g(x) = g(x) equals StartFraction one-half EndFraction x minus 2.x – 2. How does the graph of g(x) compare to the graph of f(x)?
The graph of the equation of g(x) is steeper than the graph of f(x) and has a lower y-intercept.
What is slope of a line?The ratio of how much y grows as x grows by a certain amount is called the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is.
Given that the equation of f(x) and g(x) are as follows:
[tex]f(x) = \frac{1}{4} x -1\\\\g(x) = \frac{1}{2} x -2[/tex]
Using the slope-intercept form [tex]y=mx+C[/tex], and comparing with the equations we have:
Here, m is the slope and C is the y-intercept.
Slope of f(x) = [tex]\frac{1}{4}[/tex]
Slope of g(x) = [tex]\frac{1}{2}[/tex]
y-intercept of f(x) = -1
y-intercept of g(x) = -2
The slope of g(x) is greater than the slope of f(x), also, the y-intercept of g(x) is less than the y-intercept of f(x).
Hence, the slope of g(x) is steeper than f(x) and has a lower y-intercept.
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HELP QUICK!!!
Find the distance between the two points. If necessary, round to the nearest tenth.
P(-3,-2) and Q(5,1)
Answer:
8.5440037453175 or 8.5 since the directions say to round, if necessary. Please let me know if you have any questions about this! Also, please mark brainliest! Thanks so much and have a blessed day!
Answer:
8.5
Step-by-step explanation:
Answer in the diagram
Estimate how long it would take an investment of £100 to double with a compound interest rate of 3%. Then use your answer to see exactly what the answer would be after that many years. T = 72/3 = 24 So it would take approximately 24 years to double an investment at a 3% compound interest rate.
It would take 23.45 years to double the investment of £100 with a compound interest rate of 3% to £200.
How to find the number of years to double an investment?Using the formula A = P(1 + r)^t
Initial amount of investment, P = 100
Final amount(double the investment), A = (2 x 100) = 200
Interest rate, r = 3% = 0.03
Number of years, t = ?
A = P(1 + r)^t
200 = 100 (1 + 0.03)^t = 100(1.03)^t
Divide both sides by 100
200/100 = 100(1.03)^t/100
2 = (1.03)^t
In2 = t In(1.03)
t = In2/In(1.03)
t = 23.45 years
The amount of time it would take to make £200 from £100 is 23.45 years at a compound rate of 3% using the rule of 72 and the simple interest formula.
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Calculate the surface area to volume ratio of each prism
For shape A the area to volume ratio is 101: 66
For shape B the area to volume ratio is 197117.7 : 207034
For shape C the area to volume ratio is 202.71 : 529.2
What is area and volume?The area is the amount of space occupied by a two-dimensional flat object in a plane. Volume is defined as the space occupied by a three-dimensional object. The unit of area is in square units. The unit of volume is in cubic units.
For shape A, the area = 2(lh+lb+bh)
= 2( 2×12+12×5.5+5.5×2)
= 2 ( 24+ 66+ 11)
= 2 ( 101)
= 202m²
The volume of shape A = l×b×h = 2× 12× 5.5 = 132m³.
Therefore the ratio of area to volume of shape A = 202:132 = 101: 66
For shape B
The area of the cylinder = 2πr(r+h)
= 2×3.14× 28( 28+84.1)
= 197117.7m²
The volume of the cylinder =πr²h = 3.14×28²×84.1
= 207034
Therefore the ratio of area to volume = 197117.7 : 207034
in the third shape
The area = ½bh×2 + lb+lh+bh
=6.8×7.5+ 7.2×6.8+ 7.2×7.5+ 7.5×6.8
= 48.75+48.96+54+51 = 202.71
The volume of the shape= base area × height
= 7.2×6.8×7.5
= 529.2m⅗
Thereore the area to volume ratio is 202.71:529.2
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Why is -3 a solution to 1 over 3x - 6 = -7
The solution of (1/3x) -6 = -7 will be -1 / 3.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (1/3x) -6 = -7. The expression will be solved as below:-
(1/3x) -6 = -7
1 / 3x = -7 + 6
1 / 3x = -1
x = -1 / 3
Hence, the solution of the expression for the value of x will be -1 / 3.
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8 dm to 3.2 dm
as fraction
helpp pls
The value of 8dm to 3.2 dm as a fraction is 2 1/2.
How to illustrate the fraction?It is important to note that a fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
8dm to 3.2 dm as a fraction will be simply be gotten by dividing the values that are given in the question.
In this case, this will be Illustrated as:
= 8 / 3.2
= 80 / 32
= 5 / 2
= 2 1/2
Therefore, the fraction is 2 1/2.
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The points shown on the graph represent the numbers
in a geometric sequence.
What is the initial value of the sequence?
1
2
3
8
What does 3/4 + 1/2 =
What does 1/2 x 1/2 =
Determine the coordinates for the midpoint of a segment with the following endpoints: (12,-8) and (8,-4). Answer ___________
A. (-10,6)
B. (6,-10)
C. (-6,-10)
D. (10,-6)
The value of 3/4 + 1/2 is 5/4, 1/2 x 1/2 =1/4 and Midpoint of a segment with the endpoints (12,-8) and (8,-4) is (10, -6
What is Fraction?A fraction represents a part of a whole.
We have to find the value of 3/4 + 1/2
LC of 4 and 2 is 4
(3+2)/4
3/4 + 1/2 =5/4
1/2 x 1/2 =1/4
Midpoint of a segment with the endpoints: (12,-8) and (8,-4).
Midpoint=(12+8/2, -8-4/2)
=(10, -6)
Hence, the value of 3/4 + 1/2 is 5/4, 1/2 x 1/2 =1/4 and Midpoint of a segment with the endpoints (12,-8) and (8,-4) is (10, -6)
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