The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
What is a graph?A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.
For k=- 5, y=f(x) + k represents a vertical shift down.
For h=4, the horizontal shift left is y=f(x+h).
Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
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An open cylindrical tank of radius14 m and height 3m is made of sheet metal.
(i) How much sheet of metal is required
(ii) How many litres of water can this tank hold?
(iii) What would be the cost of whitewashing this tank at the rate of ₹ 105. 5 per 2?
(i) 263.9 meters sheet of metal is required.
(ii) 1847.25 liters of water can this tank hold.
(iii) Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.
Given that,
A open cylindrical tank of radius 14 meters and height 3 meters is made of sheet metal.
We have to find
(i) The quantity of metal sheet needed.
(ii) How much water this tank is capable of holding.
(iii) How much would it cost to whitewash this tank at a rate of 105.5% per square foot?
We know that,
(i) To find the sheet required of metal is
Curved surface area of cylinder =2πrh
Here,
r is 14 and h is 3
=2π(14)(3)
=84π
=263.9
Therefore, 263.9 meters sheet of metal is required.
(ii)To find how much liters of water can tank hold.
Volume of the cylinder =πr²h
=π(14)²(3)
=588π
=1847.25
Therefore, 1847.25 liters of water can this tank hold.
(iii) To find the cost of whitewashing this tank at the rate of rupees 105.5 per 2.
=263.9×105.5
=27841.45
Therefore, Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.
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You have 10lbs of bananas after peeling the bananas you 3lbs. 6oz. Of banana peels. What is the yield percent
15. Find the perimeter of the triangle.
2х + 1
3x
X
Answer:
6x + 1
Step-by-step explanation:
When you are finding the perimeter of any shape, you will combine the measurements of each side together. Note any variables when combining. They must have the same amount of the same variables to be combined:
[tex]P = (2x + 1) + (3x) + (x)\\P = (2x + 3x + x) + 1[/tex]
Combine like terms. Add 3x, 2x and x together:
[tex]P = (2x + 3x + x) + 1\\P = (6x) + 1\\[/tex]
The perimeter of the triangle is 6x + 1.
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The 7th grade Science classes are raising money for charity. Their goal is $750.00
class has raised 50% of the total needed to meet the goal of $750.00.
class has raised one-third of the amount of their goal of $750.00
.How much more money is needed to reach their goal of $750.00?
Point K i on line egment \overline{JL}
JL. Given JL=x10,JL=x10, KL=4x,KL=4x, and JK=2x,JK=2x, determine the numerical length of \overline{KL}. KL
If the value of x will be 2. Then the length of KL will be 8 units.
What does cooperation with an example mean?
Being ability to use your body properly while moving around and cooperating with other people or things is the concept of coordination.
A gymnast walking on a tightrope without falling is an illustration of coordination. Working together to arrange or coordinate a party is an example of coordination.
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x.
Then the value of x will be
JL = JK + KL
x + 10 = 2x + 4x
5x = 10
x = 2
Then the length of KL will be
KL = 4x
KL = 4 (2)
KL = 8 units
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The complete question is-
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x,
determine the numerical length of KL.
If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
Independent-samples t test statistical test is most appropriate for analyzing the results .
What is Independent-samples t test?
To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups.
An example of a parametric test is the Independent Samples t Test. The Independent t Test is another name for this test.
What is the difference between a dependent and independent samples t-test?
If the participants in one sample do not influence the participants in the other, then the two (or more) samples are said to be independent.
Dependent samples are two (or more) samples where the members picked for one sample automatically determine the members chosen for the second sample.
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Gavin observed 22 flowers on each block of his neighborhood. Each block has an equal number of flowers. Is this sample of the flowers in the neighborhood likely to be biased?
Yes, this sample of the flowers in the neighborhood is likely to be biased. This is because the number of flowers observed on each block is relatively small and may not be representative of the entire neighborhood.
What is neighborhood?A neighborhood is a local geographic area typically containing a cluster of families and individuals who live nearby and interact with each other. It is usually a residential area, although some neighborhoods may be mixed-use, containing both residential and commercial buildings. Neighborhoods are typically identified by geographical boundaries such as a street, a park, or a body of water. People living in a given neighborhood often share certain characteristics including socio-economic status, culture, ethnicity, and even language. Neighborhoods play an important role in the lives of individuals and families, providing a sense of belonging, safety, and identity.
Additionally, if there is any external factor that influences the number of flowers on certain blocks (such as the amount of sunlight or water) then the sample may be skewed.
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2x - 5y = 23 and -4x + 5y = -11 solve by elimination
Answer: x= -1 y= -5
Step-by-step explanation: Multiply by 2 to eliminate the x
4x - 10y = 46
-4x + 5y = -11
-5y = 35
y= -5
Put -5 back in the equation for the letter y, and you will get x = -1
1. predict whether you think this a fair game or not. explain your response. a. play the game 5 times. b. now do you think the game if fair or not? ju
A game that has an equal probability of winning or losing is said to be fair.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.
A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.
Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.
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Does 2x-4=x+1+x have exactly one solution
let x and y be independent gaussian distributed random variables each with zero mean and unity variance. define the gaussian process:
As per the gaussian distributed random variables , the joint probability density function of the given variable is E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]
Gaussian distribution:
In statistics, the Gaussian distribution refers the normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
Given,
Here we need to find the the joint probability density function of the variables x and y be independent gaussian distributed random variables each with zero mean and unity variance.
Here we know that every weighted sum of the samples of the Gaussian process Z(t) is Gaussian, Z(t1), Z(t2) are jointly Gaussian random variables. Hence we need to find mean, variance and correlation co-efficient to evaluate the joint Gaussian PDF.
Then the equation is written as,
=> E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]
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The radius of circle S is half the radius of circle L. The radius of circle L is 8 millimeters.
Which measurement is closest to the area of circle S in square millimeters?
Area of the circle S be 16π square. millimeter
What is an area of circle ?
The area of a circle is the space the circle occupies in the two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. A unit area is a unit square. Examples: m2, cm2, in2, etc. Circle area = π[tex]r^{2}[/tex]in square units (Pi)π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. This is a special mathematical constant.
It is given that the radius of circle S is half the radius of circle L and the radius of circle L is 8 millimeters.
Radius of the circle S = 8/2 = 4 millimeters
Area of the circle S = π[tex]r^{2}[/tex] = π[tex](4)^{2}[/tex] = 16π square. millimeter
Therefore, area of the circle S be 16π square. millimeter
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Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y = 25 + 5h, where y represents his total earnings and h represents the number of hours he works. What does the flat pay of $25 represent in this situation?.
The $25 represent the constant for the equation y=25+5h where she lawns for $25 each lawn, plus $5 for every hour she spends mowing.
What is constant?A constant is a value or number that is consistently the same regardless of how it is expressed. For instance, in the a forementioned figure, when its face value is 36 and 82 respectively, 36 and 82 remain constant. Its worth remains constant. A constant in mathematics is a particular number or symbol that has been given a stable value. In other words, a constant is an expression-unchanging value or integer. It always has the same value.
Here,
The $25 serves as the constant in the equation y=25+5h, where she charges $25 for each lawn she mows and an additional $5 per hour.
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These are the times for 200 people to get to work
time people
0
10
30
40
50
A 10% sample, stratified by time, is taken.
complete the table
time people
0
10
30
40
50
got to work out the number of people using the same time
please help
The entries that complete the table are 1, 2, 8, 6 and 3.
Given:
These are the times for 200 people to get to work time people. A 10% sample, stratified by time, is taken.
Complete the table :
To do this, we multiply the number of people by the proportion of sample i.e. 10%.
The product is then approximated to the nearest unit
So, we have:
7 => 7 * 10 % ≈ 1
22 => 22 * 10 % ≈ 2
77 => 77 * 10 % ≈ 8
63 => 63 * 10 % ≈ 6
31 => 31 * 10 % ≈ 3
Hence, the entries that complete the table are 1, 2, 8, 6 and 3.
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PLEASE HELP! THANK YOU
Answer:
1. A repeating decimal is a fraction [tex]\frac{a}{b}[/tex] where a and/or b are fractions and b is not equal to 0.
2. A decimal that ends is a ( n ) terminating decimal
3. Two numbers that have a sum of 0 are additive inverses
Which of the following constructions must you know how to do in order to construct an inscribed circle for a given triangle?
angle bisector
perpendicular bisector
duplicating a line segment
bisecting a segment
For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).
What is an angle bisector?The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.
The diagram for the given case can be drawn as follows,
For the circle inscribed in the circle, all the sides are tangents.
By the property of tangents to a circle ∠ODB and ∠OFB are right angles.
Now, in ΔODB and ΔOFB the relation is obtained as,
∠ODB = ∠OFB (right angles)
OB = OB (Common sides)
And, OD = OF (radius of the circle)
⇒ ΔODB ≅ ΔOFB (by RHS criteria)
This implies that ∠ODB ≅ ∠OFB.
Thus, the line joining the centre and the vertex of triangle bisects its angles.
Hence, for the given case the required construction to be known is the angle bisector of triangle.
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Explain how a number line is used to determine the sum of -3 + 7
Explanation about number line is discussed below:
What is number line?Number lines are horizontal straight lines used in mathematics when integers are spaced at equal intervals. A number line may be used to visualise all the numbers in a succession. Both endpoints of this line continue forever.
Number lines aid in the development of a mental arithmetic approach for addition and subtraction. Research has proved the significance of number lines in fostering sound mental number sense and arithmetic techniques. No one disputes the significance of number lines.
Firstly, start from -3 on the number line.
Then, since we are adding 7, we would add 7 spaces to the right.
That should lead us to our answer; 4.
Another way is: 7 + (-3) or 7-3.
They all equal 4.
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This weekend, Jerome earned 252.50 in all. What was the dollar amount of the meals that Jerome served?
Jerome served $
worth of meals this weekend.
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
Given: The total amount Jerome earned this weekend is $252.50.
He earned every weekend = $80.
He earned 15% of the cost of meals as tips by serving them.
To find: The cost of meals served by Jerome in this weekend.
The total amount, $252.50, is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.
Let x be the cost of meals that Jerome served this weekend.
The equation for the problem statement becomes
[tex]\$80 + \frac{15}{100} x = \$252.50\\\\[/tex]
Keeping only the x term on the left side of the equation and constant terms on the right side we get
[tex]\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\[/tex]
Multiply both the sides of the equation by 100
[tex]\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250[/tex]
Divide both sides of the equation by 15
[tex]\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150[/tex]
What is algebra?Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.
What is an equation?An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value on either side of the equal sign.
What is an algebraic expression?A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.
Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
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Can i please have help?
Analyzing the graph of the linear equation, we can see that for 1.4 grams of chemical A you will need 1.2 grams of chemical B.
How much of chemical B is needed?The amounts of chemicals A and B needed are modeled by the linear equation on the graph.
Here we want to see how much of chemical B is needed if we decide to use 1.4g of chemical A.
Chemical A is on the horizontal axis, so we need to find 1.4 on the horizontal axis, and then move upwards until we reach the linear equation, and then move to the left until we reach the vertical axis.
Doing that we can see that we will need 1.2 grams (3 little squares in the vertical axis) of chemical B.
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A, B and C are Collinear and B lies between A & C. Determine all that are true:
AB=2, AC=2x + 4, and BC = x + 6.
Find x.
OBC=10
AC=12
Segment Addition Postulate
AC-14
x=4
OBC=11
O Angle Addition Postulate
Ox=5
The required statment that is true is AC = 12 and BC = 10. Option A is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A, B and C are Collinear and B lies between A & C.
AC = AB + BC
2x + 4 = 2 + x + 6
2x + 4 = x + 8
x = 4
Now,
AC = 8 + 4 = 12
BC = 4 + 6 = 10
Thus, the required statment that is true is AC = 12 and BC = 10. Option A is correct.
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pls help due now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 9x = 18
Step-by-step explanation:
4x - y + 5x + y = - 3 + 21
9x = 18
x = 2
Simplify (4 xy) (−2x)
Answer:
-x2 y
Step-by-step explanation:
A student raises her grade average from a 75 to a 90. What was the percent of increase in the
student's grade average? Round your answer to the nearest tenth of a percent, if necessary,
20%
016.7%
08.3%
015%
Answer:
Step-by-step explanation:
D: 15%
find the probibility that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating
The probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.
Explain the term binomial probability?A binomial experiment can have two possible outcomes: success or failure, and the term "binomial probability" refers to the likelihood of obtaining precisely x successes upon n repeated but independent trials. The probability of success on a single try is p, and the formula for the binomial probability is as follows:P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣLet X represent a random variable which represents the proportion all school graduates who secure employment in their profession of choice within a year of graduation:
With a binomial distribution,
X has a n = 5 and a p value of 0.57.
n = number of trial.
p = probability of success
x = number of success.
A binomial distribution's probability mass function is provided by:
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The likelihood that at least one gets employment in their field of choice within a year after graduation:
P(X ≥ 1) = 1 - P(X < 1)
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - ⁵C₀ . (0.57)⁰ . (0.43)⁹⁻⁰
P(X ≥ 1) = 1 - 0.603
P(X ≥ 1) = 0.9396
P(X ≥ 1) = 93.96%
Thus, the probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.
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The complete question is-
A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
A car is traveling at a rate of 48miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in 15 minutes?
Answer:
12 miles in 15 minutes
Step-by-step explanation:
To find the car's rate in miles per minute, we can divide the rate in miles per hour by the number of minutes per hour. There are 60 minutes in an hour, so the car's rate in miles per minute is 48 miles per hour / 60 minutes per hour = 0.8 miles per minute.
To find the number of miles the car will travel in 15 minutes, we can multiply the rate in miles per minute by the number of minutes. The car will travel 0.8 miles per minute * 15 minutes = 12 miles in 15 minutes.
Fill in the blank
The _________of a number is the distance between the number and zero on a number line
The distance on the number line between a number and 0 is its absolute value.
What is number line?The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line.
When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them.
One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero.
In other words, as we move to the right on a number line, the value of the numbers increases.
The part of the number line to the left of zero is called the negative number line. But all is in the region to the right of zero.
Hence, The distance on the number line between a number and 0 is its absolute value.
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What is the 3n^2 first 4 terms and the 10th term?
Answer:
a1=3 ;a2=12 ;a3=27 ;a4=48 ;a10=300
Step-by-step explanation:
an=3n^2
a1=3(1)^2
a1=3
a2=3(2)^2
a2=12
a3=3(3)^2
a3=27
a4=3(4)^2
a4=48
a10=3(10)^2
a10=300
Simplify: 5m + 3b - 9m - 4w Responses 14m + 7b 14m + 7b 14m + 3b - 4w 14m + 3b - 4w -4m + 3b - 4w -4m + 3b - 4w 21
Answer:
3b-4w-4m
Step-by-step explanation:
3b-4w+5m-9m
3b-4w-4m
Answer:
-4m+3b-4w
Step-by-step explanation:
5m+3b-9m-4w
we combine like terms but in this case only the m are like terms
5m-9m+3b-4w
-4m+3b-4w
i cant really see the options but it looks like it is the second to last or c option
hopes this helps please mark brainliest
The sum of two numbers is 45
and their difference is 5.
What are the two numbers?
Larger number
1
Smaller number
Answer: 20 and 25
Step-by-step explanation: we know that there are 2 numbers and the sum is 45. Let's put one number as x. The other number is x+5 because the difference is 5. So our equation is- x+x+5=45. After we solve the equation by subtracting 5 from each side and simplifying x, we get x=20. The other number should be 5 more so the second number is 25. The numbers are 20 and 25. Please rate this answer!
Please help me solve!
Answer:
13.5%
Step-by-step explanation:
Given that μ = 144, σ = 27:
For x = 90: z= 90-144/27=-2
For x = 117: = 117-144/27 = -1
Therefore, From the normal distribution table: -2 gives .02275 and -1 gives .15866
So the required percentage = .02275 - .15866 = -0.13591= 13.5%
Hence, 13.5% of the population would be between 144 and 198