Answer:
Step-by-step explanation:
(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.
The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.
(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.
(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.
The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.
(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.
So, the new variance is 6^2 * V = 36 * V.
--------
Here is a definition of each variable:
μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.
σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.
V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.
c: A constant value added to each data point.
k: A constant value multiplied to each data point.
In the diagram below, point O is the center of the circle.
C
A
(2x+5)°
0
B
Use the given information in the diagram to determine the value of x.
The value of x for the angle C in the triangle ABC is equal to 42.5
What is a triangle formed by a circle diameterA triangle formed by the diameter of a circle is a right triangle, with one side being the diameter of the circle and the other two sides being radii of the circle. Since the diameter of a circle bisects the circle into two equal halves, it also bisects the right angle formed by the radii into two equal angles of 45 degrees each.
The angle C is equal to 90° and we shall solve for the value of x as follows:
2x + 5 = 90°
2x = 90° - 5 {subtract 5 from both sides}
2x = 85°
x = 85°/2 {divide through by 2}
x = 42.5
Therefore, the value of x for the angle C in the triangle ABC is equal to 42.5
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In-State tuition at UNCW is currently
$6,691. NC is raising tuition 1% each year for the next 4 years. What will be the new tuition 4 years from now?
The new tuition 4 years from now is $6962.68.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$6691, rate of interest=1% and time period=4 years.
Now, A=6691(1+1/100)⁴
=6691(1+0.01)⁴
=6691(1.01)⁴
= 6691×1.04060401
= $6962.68
Therefore, the new tuition 4 years from now is $6962.68.
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Population increase in India India had one billion people in 2001. Its growth rate was 1.8% per year. By how many people did the population increase the first year?
The population increased by 18 million at the end of one year at the rate of 1.8%.
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. Alternatively put, it is the relationship between a component and a whole in which the value of "whole" is always assumed to be 100.
For instance, if a student receives 15 out of 50 in math, one can determine the relevant percentage by expressing "marks earned" as a fraction of "total marks" and multiplying the result by 100. i.e., the percentage of marks is equal to 15 / 50 100, or 30%.
Given that, population of India is one billion.
The rate of increase is 1.8%.
After one year the population will be:
P = (1000000000)(1.8/100)
P = 18000000
Hence, the population increased by 18 million at the end of one year at the rate of 1.8%.
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x/q = -5
solve the equation
Answer:
It could be [tex]x=25[/tex] and [tex]q = -5[/tex] or it could be [tex]x=-25[/tex] and [tex]q = 5[/tex]. As both x and q are variables, either of these could be correct.
Solve for x:
-4x + 2(x+4)= -7x- (x + 1)
Answer: x = -3/2
Step-by-step explanation:
-4x + 2(x+4) = -7x - (x+1)
-4x + 2x+8 = -7x -x-1
-2x + 8 = -8x - 1
+2x +2x
8 = -6x - 1
+1 +1
9 = -6x
/-6 /-6
-9/6 = x
-3/2 = x
Solve the triangle. Round to the nearest tenth.
In the given triangle, ∠F=29°, d>15 and e<15.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now
As sum of all angles of triangle=180°
∠F+127°+24°=180°
∠F=180-151
∠F=29°
and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.
Then the sides e and d will be as following d>15 and e<15.
hence,
In the given triangle, ∠F=29°, d>15 and e<15.
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Please help!
An object is dropped from the top of a tower with a height of 1170 feet. Neglecting air resistance, the height of the object at time
t seconds is given by the polynomial -16t² +1170. Find the height of the object at t=2 seconds.
The height of the object at 2 seconds is _____ feet.
The height of the object at a time of 2 seconds is given as follows:
1106 feet.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
h(t) = -16t² + 1170.
At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:
h(2) = -16(2)² + 1170
h(2) = 1106 feet.
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A researcher tested two groups (females and males) of rats on memory performance. The following scores are for the number of correct choices they made on the task:
The probability distribution does not add up to 1.0, in other words.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.The study of events susceptible to probability is known as statistics. The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes.This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).Probability can be divided into four main categories: axiomatic, axiomatic, classical, and empirical. The area of mathematics known as probability studies the likelihood that a random event will occur.The complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
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Answer:
It is not accurate
Step-by-step explanation:
If the complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
THEN:
To determine whether the probability distribution is accurate, we need to check two conditions:
The sum of the probabilities should be equal to 1.
All probabilities should be between 0 and 1.
Let's check these conditions:
Sum of probabilities:
p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05
The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.
All probabilities should be between 0 and 1:
The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.
However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.
Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.
Consider the line 8x-5y=1
what is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line
Answer:
[tex]\frac{8}{5}[/tex] and - [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
8x - 5y = 1 ( subtract 8x from both sides )
- 5y = - 8x + 1 ( divide through by - 5 )
y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{1}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{5}[/tex]
• Parallel lines have equal slopes
then the slope of a parallel line is m = [tex]\frac{8}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{5} }[/tex] = - [tex]\frac{5}{8}[/tex]
Jesus believes in looking his best when searching for a job. He wants to save $435 for a new suit for his interviews. He currently has $65.00 and he can save $18.00 per week from his work.
How many weeks in total will it take him to save for the suit, assuming he puts the $65.00 into an account on week 1 and starts saving each week thereafter?
Answer:
6.7 weeks.
Step-by-step explanation:
65.00 x 6.7 = 435.50
Answer:
Step-by-step explanation:
He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5
not mine but he did he get it right
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.
a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.
From the problem statement, we know that:
2x + y = 10 (jog around the block twice and the park once in 10 minutes)
2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)
These are the two linear equations that represent the given situation.
b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.
We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:
(2x + 3y) - (2x + y) = 22 - 10
2y = 12
y = 6
So, it takes 6 minutes to jog around the park.
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Complete question:
You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.
a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:
b. how long does it take you to jog around the park? it takes you minutes to jog around the park.
What is the simplest form of
x^2+ 5x-36/
X^2-16
?
Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.
The statement that correctly defines continuous and discrete quantitative variables is:
"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."
A variable is a quantity that may assume any one of a set of values.
This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.
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Solve the system by graphing.
a)
y = x
y = 2x+2
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
Solving the system of equations:To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.
In the next step, we need to Identify the solution to the system.
If the lines are intersected, the point of intersection is the solution.
If the lines are parallel, the system will have no solution.
If the lines are the same or coincident, then the system will have an infinite number of solutions.
Here we have
y = x ----- (1)
y = 2x+2 ---- (2)
From (1) and (2)
=> y = 2y + 2
=> 2y - y = -2
=> y = - 2
Hence, the solution of the given system of the equation is (-2, -2)
We can check it by graphing the lines as shown figure.
Therefore,
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
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Taking the earth to be the sphere of radius 6378000m, find the circumference of the equator of the earth. Give your answer in km and in terms of pi.
Answer:
12756pi km
Step-by-step explanation:
Circumference = pi * diameter
Diameter = radius * 2
kilometer = meter/1000
6378000*2= 12756000
diamter = 12756000 meters
12756000/1000 = 12756 kilometers
diameter = 12756 kilometers
12756pi km= circumference
A road is inclined at an angle of 6 . After driving 4950 feet along this road, find the driver's increase in altitude.
The driver increased altitude is 517 feet.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the road is inclined at an angle of 6 degrees. After driving 4950 feet along this road, let's find the altitude as follows:
using trigonometric ratios,
sin 6° = opposite / hypotenuse
Therefore,
sin 6° = a / 4950
cross multiply'
a = 4950 sin 6°
a = 4950 × 0.10452846326
a = 517.415893175
Therefore,
a = 517 feet
Altitude = 517 feet
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pls help with this
Find the length of side x in simplest radical form with a rational denominator.
The length of x is 6 in the given triangle.
What is Trigonometry?The branch of Mathematics which studies relationships between side lengths and angles of triangles.
We have to find the value of x in the given triangle.
We know that tan theta is the ratio of opposite side by adjacent side.
The opposite side is x and the adjacent side has √12
tan60=x/√12
√3=x/√12
x=√12√3
x=√36
x=6
Hence, the length of x is 6.
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A total of 360 people voted in an election. The circle graph shows the results.
(a) How many people (number of people, not the percentage) voted for Goron?
Show your work.
(b) How many people (number of people, not the percentage) voted for Fishman
and Other? Show your work. PLEASE HELP
a. There were 126 people who voted for Goron.
b. There were 144 people who voted for Fishman.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given circle graph shows the results.
There were 360 people who voted in the election.
According to the question, the required solution would be as:
number of people who voted for Goron = 35% of 360
15% is expressed as 15/100 in fractional form
number of people who voted for Goron = (35/100) × 360
number of people who voted for Goron = 126
number of people who voted for Fishman = 40% of 360
number of people who voted for Fishman = (40/100) × 360
number of people who voted for Fishman = 144
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The missing figure has been attached below
HELPPPPPP
find each value
Answer: x=4, AB=19, ED=57
Step-by-step explanation:
Trapezoid midsegment formula: [tex]\frac{b1+b2}{2}[/tex]=Midsegment
Therefore, (4x+3+18x-15)/2=38
Multiply both sides by 2 in order to get rid of the fraction. (Multiplication property of equality)
4x+3+18x-15=76
Combine like terms.
22x-12=76
Add 12 to both sides. (Addition property of equality)
22x = 88
Solve for x
x = 4
Now, substitute x in for segment AB and ED
AB = 4(4)+3
AB= 16+3
AB= 19
ED=18(4) -15
ED=72-15
ED=57
Check your work:
(ED+AB)/2 = 38
(57+19)/2 = 38
76/2 = 38
38 = 38
In Iceland, the temperature drops when the sun goes down. The temperature at 5:00 is 5°C. By 9:00, the temperature had dropped 24°. If the temperature dropped at a constant rate, how much did it drop per hour?
If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).
Find the sum of 4√5 and √5 in simplest form. Also, determine whether the result is
rational or irrational and explain your answer.
Answer:
See below
Step-by-step explanation:
[tex]4\sqrt{5}+\sqrt{5}=(4+1)\sqrt{5}=5\sqrt{5}[/tex]
This sum is irrational because [tex]\sqrt{5}[/tex] was irrational to begin with.
Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
From given graph we can see that
At x=2, the function in the graph is approaches to infinity.
It means function is not defined at x=2
We know that a rational function is undefined when denominator is equal to zero.
For equation 1:
f(x)= 2(x+2)/(x-2)
Equating the denominator:
x-2=0
x=2
It means function is not defined at x=2
The y-intercept is: y= -2
The function is passing through the point (1,-6).
When we substitute x=1
Hence, option 1 is true.
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See attached image and answer questions.
The properties of the polynomial are
Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1How to determine the properties of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2Using the above as a guide, we have the following:
Degree = sum of multiplicities
Degree = 1 + 1 + 2 + 1
Degree = 5
The leading coefficient is negative
This is so because the graph opens down
There are 3 zeros with odd multiplicities and 1 zero with even multiplicity
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PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:15n + 3 = 153
Step-by-step explanation:
15n + 3 = 153
product of 15 and a number n is 15n, and 3 more gets the plus 3, and it said all of this is 153
n=10 also as subtract 3 both sides then get 15n=150 get n by itself by dividing both sides by 15 and get n=10
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
RECAP NEED HELP STILL
Using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.
What is a right-angled triangle?
A right triangle, also known as a right-angled triangle, is a triangle with one right angle, or two perpendicular sides. The sum of the other two angles is 90 degrees.
In all of these figures, one of the angles is 90°. So we can use Pythagoras' theorem and trigonometric relations, to solve the questions.
1) Opposite side = 5
sin 27° = Opposite side/ hypotenuse
0.45 = 5/x
x = 11.11
2) Hypotenuse = 16
cos 63 = adjacent side/hypotensue
0.45 = x / 16
x = 7.2
3) Hypotenuse = 29
sin 67 = opposite side/hypotensue
0.92 = x/29
x = 26.68
4) Opposite side = 27
tan 39° = opposite side/ adjacent side = 27/x
0.81 = 27/x
x = 33.33
5) sin Q = opposite side / hypotensue = 14/50 = 7/25
sin R = opposite side / hypotensue = [tex]\sqrt{50^2 - 14^2}[/tex]/50 = 48/50 = 24/25
cos Q = PQ/ 50 = 48/50 = 24/25
cos R = PR/50 = 14/50 = 7/25
tan Q = sin Q/cos Q = 7/24
tan R = sin R/cos R = 24/7
Therefore using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.
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NEED HELP ASAP PLEASE! The table below represents a linear function. What is the slope of the graph of this function?
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
A: 2
B: -1/2
C: 1/2
D: -2
The slope of the graph of this function is 1/2, the correct option is C.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We are given that;
The x input and y output of function.
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
Now
m=y2-y1/x2-x1
m= 2-1/5-3
m=1/2
Also, m=-1+2/-1+3
m=1/2
Therefore, the slope of the function will be 1/2
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PLEASE HELP!!!
A survey was conducted in which the customer service representatives of two companies were rated on a scale of 1 to 6. The graph below shows customer service ratings of 20 representatives. The interquartile range for each company is 3. The difference between the median rating for each company is approximately how many times the interquartile range?
The difference between the median rating for each company is approximately 0.3 times the interquartile range.
How to calculate the median service rating?Generally speaking, the median for 20 observations is the average of the 10th and 11th number:
Median rating of Company A = (4 + 4)/2
Median rating of Company A = 8/2
Median rating of Company A = 4.
Median rating of Company B = (3 + 3)/2
Median rating of Company B = 6/2
Median rating of Company B = 3.
Difference in median = 4 - 3
Difference in median = 1
For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:
1 = 3x
x = 1/3.
x = 0.3
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Graph the linear inequality.
x < 2
What does a rising sequence do in a piece of music?
A. Increases the dynamic
B. Adds drama and tension
C. Decreases the dynamic
D. Decreases the tempo
