The coordinates of the figure after the rotation of 180° will result in a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the figure be represented as JKL
Now , the rotated figure be represented as J'K'L'
The coordinates of JKL be J ( x₁ , y₁ ) , K ( x₂ , y₂ ) and L ( x₃ , y₃ )
Now , let the rotation angle be d = 180°
For a rotation of 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
Substituting the values in the equation , we get
The coordinates of J'K'L' is J' ( -x₁ , -y₁ ) , K' ( -x₂ , -y₂ ) and L' ( -x₃ , -y₃ )
Hence , the rotation is solved
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Sally saved $182 in March. Her father gave her $20 for every
$50 she saved. How much did Sally's father give her?
Answer:
72.8 or 72 4/5
Step-by-step explanation:
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 108 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.
Answer:
Step-by-step explanation:
Find the probability that X is less than 92:
We can use the cumulative distribution function (CDF) of a normal distribution to find the probability that X is less than 92. The CDF of a normal distribution with mean μ and standard deviation σ is given by:
F(x) = (1/2) * [1 + erf((x-μ)/(σ * sqrt(2)))]
Where erf is the error function.
So, the probability that X is less than 92 can be calculated as:
P(X < 92) = F(92) = (1/2) * [1 + erf((92-108)/(17 * sqrt(2)))]
This value can be calculated using a calculator or statistical software.
Find the probability that X is between 92 and 126:
We can use the CDF to find the probability that X is between 92 and 126. The probability that X is between 92 and 126 is equal to the difference between the CDF values at 126 and 92:
P(92 < X < 126) = F(126) - F(92)
This value can also be calculated using a calculator or statistical software.
Find the IQ of an individual that is in the top 10% of the population:
To find the IQ of an individual that is in the top 10% of the population, we need to find the value of X that corresponds to a cumulative probability of 0.9. This can be done by solving for X in the CDF equation:
F(X) = 0.9
X = μ + σ * inverse_CDF(0.9)
Where inverse_CDF is the inverse cumulative distribution function and can be calculated using a calculator or statistical software. The value of X that corresponds to a cumulative probability of 0.9 is the IQ of an individual that is in the top 10% of the population.
decide which of the two given functions is linear and find its equation.x=0,1,2,3,4f(x)=6,10,14,18,22g(x)=8,10,12,16,22
The function f(x) is linear and equation is y = 4x + 6 where x=0,1,2,3,4
What exactly is a function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a co-domain, as well as a range. In general, a function is denoted as f(x), where x represents the input. A function's generic representation is y = f(x).
In mathematics, there are several types of functions. Some examples include:
When there is a mapping for a range for each domain between two sets, this is referred to be an injective function or a one to one function.
Surjective functions, also known as Onto functions, are used when more than one element is transferred from domain to range.
Polynomial function: A function made up of polynomials.
Inverse Functions: A function that may be used to inverse another function.
Now,
For function f(x)=6,10,14,18,22, g(x)=8,10,12,16,22 for x=0,1,2,3,4
f is a function because y increases 4 for each increase of 1 in x
slope = 4
intercept = f(0) =6
Hence Equation is y = 4x + 6 where x=0,1,2,3,4
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Numbers in thousands) of forest fires over the year and the number in hundred thousands) of acres burned for 7 recent years are shown.Number of fires x | 69 58 47 84 62 57 72Number of acres burned y | 64 53 42 79 57 52 67The correlation coefficient for the data is r = 1 and a = 0.05. Should regression analysis be done?The regression analysis (should/should not) be done.
The correlation coefficient of 1 indicates a strong positive linear relationship between the number of forest fires and the number of acres burned.
However, the correlation coefficient alone does not determine if regression analysis should be done or not. Other factors such as the purpose of the analysis, the distribution of the data, and the presence of outliers should also be considered.
In general, if the relationship between the two variables is of interest and there is sufficient evidence of a linear relationship, then regression analysis may be appropriate. However, a final decision requires a deeper understanding of the problem and the data.
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How do I solve this?
Solve for x and y then use pythagorean theory
Answer:
x = (10.392)
y = 12
Step-by-step explanation:
Trigonometric Functions:Trigonometric Functions are special functions relating to the ratio of the sides of triangles. There are 6 primary ones known as sin, cos, tan, csc, sec, cot which all have definitions relating to the sides of a triangle.
We want to use one where it's defined using the adjacent side and opposite side since we know the adjacent side (the side 6) we just don't know the opposite side (the x side).
Luckily we have a function tan which is defined as: [tex]tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}[/tex]
We can plug in values we know: [tex]tan(60) = \frac{x}{6}[/tex] now just multiply both sides by 6 to solve for the x value: [tex]tan(60) * 6 = x[/tex] and then using a calculator we get approximately: 10.392 and now from here we can use Pythagorean Theorem:
[tex](10.392)^2 + 6^2 = y^2\\\\107.994 + 36 = y^2\\\\143.994=y^2\\\\12=y[/tex]
Step by Step please, list all information given by the marks on the diagram.
Answer:
C
Step-by-step explanation:
(4x + 1) and 57 are vertically opposite angles and are congruent, so
4x + 1 = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14
Question Help: How much should be invested today at 6.25% compounded quarterly to have $18,000 in 13 years?
When 6.25% is compounded quarterly to get $18,000 in 13 years, the total amount is $22,478.16 in compound interest.
what is interest ?Divide the total by the yield curve, the length of time, and other factors to arrive the simple interest. Simple return = money + return + hours is the marketing formula. This method allows it easiest to calculating interest. The most typical technique to figure approximately interest is as a portion of the principal sum. He will only pay his share of the 100% extra, for example, if he borrows $100 from a neighbor and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow, you must pay interest, and when you give it out, you must charge interest. Interest is often determined like an indicator of the overall of both the loan total.
given
Amount = Principal (1 + rate of interest) number of years
= $1,200 (1 + 0.032) 8
= $1,200 1.286582318
= $22,478.16 is the amount in compound interest.
The remaining amount is $40,478.16.
When 6.25% is compounded quarterly to get $18,000 in 13 years, the total amount is $22,478.16 in compound interest.
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consider the following data sets: variable a: 5 3 5 5 4 8 variable b: 3 1 1 4 2 1 calculate the sample covariance.
The required sample covariance of the given sample is (C) -0.20.
What is sample covariance?The link between two random variables from the sample is measured using sample covariance, which uses a smaller sample of the population.
Working with huge populations, such as in long-term medical studies or stock investment tools, makes this statistic helpful.
So, the number of samples is:
n = 6
Then, the mean of x:
[tex]\begin{aligned}\bar{x} & =\frac{\sum x}{n} \\& =\frac{30}{6} \\& =5\end{aligned}[/tex]
The mean of y:
[tex]\begin{aligned}\bar{y} & =\frac{\sum y}{n} \\& =\frac{12}{6} \\& =2\end{aligned}[/tex]
The sample covariance:
[tex]{Cov}(x, y)=\frac{\sum\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{n-1}\\\begin{aligned}& =\frac{-1}{5} \\& =-0.20\end{aligned}[/tex]
Therefore, the required sample covariance of the given sample is (C) -0.20.
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Correct question:
Consider the following data set: Variable 1: 5 3 5 5 4 8 Variable 2: 3 1 1 4 2 1
The sample covariance for this data set is ?
a). 2.30
b). -0.20
c). 0.65
d).-1.77
Three girls share an amount of money. the eldest get b/3c of the total amount while the youngest gets b/6c of the total. what fraction does the third girl gets?
Answer:
(2c-b) / 2c
Step-by-step explanation:
b/6c + b/3c + y = 1,
Because these are fractions they must add up to 1.
Add and simplify,
(6bc + 3bc)/18c^2
b/2c + y = 1,
Make y the subject,
y = 1 - b/2c
y = (2c-b)/2c
ved Match each equation of a tangent line to the correct tangent on the graph of the function f(x) = 0.1x³ + 2. y = 0.3x + 1.8 y = 4.8x - 10.8 y = 2.7x + 7.4 - y = 2.7x+3.6 y = 1.2x + 7.4 y = 4.8x + 1.8 -2 -1 10 3 1 y = 0.3x - 10.8 f(x) = 0.1x³ + 2/ 2/ 3 y = 1.2x+3.6
y = 0.3x + 1.8 matches f(x) = 0.1x³ + 2
y = 1.2x + 7.4 matches f(x) = 0.1x³ + 2
y = 2.7x + 3.6 matches f(x) = 0.1x³ + 2
y = 4.8x + 1.8 does not match f(x) = 0.1x³ + 2
y = 4.8x - 10.8 does not match f(x) = 0.1x³ + 2
y = 0.3x - 10.8 does not match f(x) = 0.1x³ + 2
What is a tangent line?A tangent line is a straight line that touches a given curve at a single point and has the same slope as the curve at that point. In other words, it is a line that locally approximates the curve at that point. The tangent line is often used to study the behavior of a function near a particular point and can provide valuable information about the properties of the curve
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Help ASAP! Due tonight! Will mark brainliest-
This may sound wrong or confusing but I have a cousin in college and he said that it should be 3-6!
Ashley and Kendall are both downloading a large file online. Below are the numbers of seconds each has been downloading and the number of megabits downloaded. Which of these statements is true based on the given information?
PLSSSSS ANSWER NOW!!!!!!!!
Step-by-step explanation:
We would but there is no given information or numbers.
Answer:
Step-by-step explanation:
picture please
Please Help ASAP
What is the area of the polygon?
Answer:
577.95
Step-by-step explanation:
find area of rectangle and then 2 triangles
15*33=495
8*15*1/2=60
3*15.3*1/2=22.95
22.95+60+495=577.95
Point P is equidistant from both [AB] and [AC]. Use congruence to show that P lies on the bisector of BAC.
Hint: To find the distance from P to either line we draw a perpendicular from the point to the line. So, the figure becomes:
Based on the RHS rule of congruency of triangles, APC and APB are congruent, therefore, P lies on the bisector of BAC.
How can it be proved that P lies on the bisector of BAC?To prove that P lies on the bisector of BAC:
Sketch the angle and its bisector.Draw perpendiculars from any point along the bisector onto the two angles' two arms. The two arms, the bisector, and the two perpendiculars you sketched have now joined to form two triangles.Based on two equal angles (the bisected angle), right angles, and a similar side, the two triangles are said to be congruent (RHS congruence rule). As a result, the perpendiculars are of equal length, and the angle's bisector is equally spaced from its sides.
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There is a dodge ball with radius 10in and a soccer ball with radius 3in. Find how many times greater the _ volume of the dodge ball is than that of the soccer ball.It is 3.3 greater.It is 37 greater.It is 33 times greater.It is 3.7 times greater.
Option B is the correct answer. which is 37 times greater.
The volume of the sphere is defined as a measure of space that can be occupied by a sphere.
The general formula for the volume of a sphere is given:
V=4/3πr³.
where r is the radius
and the value of π is 3.17
As per the question r= 10 for dodgeball and r= 3 for the soccer ball.
substitute the values in the above formula
V₁=4/3π(10)³ and V₂=4/3π(3)³
Now divide V₁/V₂.
V=4/3π(10)³/4/3π(3)³
V=(10)³/(3)³
V=1000/27
V=37.03
so the volume of the dodgeball is 37 times greater than that of the soccer ball.
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Full question:
There is a dodgeball with a radius of 10in, and a soccer ball with a radius of 3in. Find how many times greater the volume of the dodgeball is than that of the soccer ball Select one 37 times 3.33 times 11.1 times 30 times
Tanya is training a turtle for a turtle race. For every 5/6of an hour that the turtle is crawling, he can travel 3/20 of a mile. At what rate is the turtle crawling in miles per hour?
A-59/60 of a mile per hour
B-9/50 of a mile per hour
C-1/8 of a mile per hour
D-8 miles per hour
The turtle's rate is given as follows:
B- 9/50 of a mile per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
t = 5/6, d = 3/20.
Hence the velocity is obtained as follows:
v = (3/20)/(5/6)
v = (3 x 6)/(20 x 5)
v = 18/100
v = 9/50.
Meaning that option B is correct.
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Jo borrowed $6,650 for 8 months from a bank. The bank discounted the loan at 8.5% .
a. How much interest did Jo pay the bank for the use of its money?
b. How much did he receive from the bank?
c. What was the actual rate of interest he paid?
Round interest amount to nearest cent.
The interest rate for Jo's 8-month, $6,650 bank loan was $70.14. The bank applied an 8.5% discount on the loan.
what is interest ?By divided the principal by interest rate, the duration of time, and other factors, simple interest be determined. Simple return means principal plus interest hours straight is the technique used in marketing. The quickest thing to compute interest if to use this method. The most popular way of calculating interest is as portion of the outstanding sum. For example, if he takes $100 from a buddy then agrees to repay the debt at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you need to lend money when you lend it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the term given to this percentage.
given
A = P(1 + r)ⁿ
A is the sum, P is the sum at the beginning, r is the interest rate, and n is the number of years.
Jo took out a four-month loan from a bank for 3,800. The bank applied a 5.5% discount to the loan.
The true interest rate is going to be
r = 5.5% / 12
r = 0.458%
When this happens, the money the bank gets is equivalent to what Jo paid in interest.
I = P(1 + r)ⁿ - P
I = 3800 (1 + 0.055/12)⁴ - 3800
I = $3870.14 - $3800
I = $70.14
The interest rate for Jo's 8-month, $6,650 bank loan was $70.14. The bank applied an 8.5% discount on the loan.
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an outdoor theater currently has 1,375 ft next year 125 news seats will be added there will be 25 ft in each row after the new seeing has been added how many rows would a theater have after the new seats have been added?
The total number of rows in the Theater after 125 seats are added is 60 rows.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The Outdoor theater currently has 1,375 seats.
If we add 125 new seats then the number of seats are
= 1375 + 125
= 1500
Each row have 25 seats in one row.
Then, the total number of rows in Theater
= 1500/25
= 60 rows.
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An airplane crosses the Atlantic Ocean (3000) miles with an airspeed of 5000 miler per hour
The time required to cross the airplane Atlantic Ocean is (3/5) hours.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know, Distance = Speed×Time.
Given, Distance is 3000 miles and the speed is 5000 miles per hour.
Therefore, 3000 = 5000×t.
t = 3000/5000.
t = 3/5 hours.
Q. An airplane crosses the Atlantic Ocean (3000) miles with an airspeed of 5000 miles per hour, What is the time required to cover the distance?
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A land surveyor measured these lengths to find the distance, d, across a pond.
What is d, to the nearest tenth of a meter?
A
B
C
16.0 meters
19.2 meters
20.0 meters
Q
24 m
10 m
Р
12 m
The value of AB to the nearest tenth of a meter is 21 meter.
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar, if the ratio of their corresponding sides are in the same proportion
Triangle ABC and CDE are proportional, hence:
AB / DE = AC / CE
substituting:
AB / 7 = (12 + 6)/6
AB = 21 meter
The value of AB is 21 meter.
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i need help with this problem
Answer:
1
Step-by-step explanation:
Anything to the 0 power is 1
Suppose you're given a data set the classifies each sample unit into one of four categories: A, B, C, D. You plan to create a computer database consisting of these date, and you decide to code the dat B2,C3, and D. Are the data consisting of the classifications AB, C and D qualitative or quantitative? Are the data are input as 1,2. 3. 4. are the qualitative or quantitative? Are the data consisting of the classifications AB, C, and qualitative or quantitative? O A Qualitative because they were measured on a naturally occuring numerical scale OB. Quaritative, because they can only be classified into categories OC. Qualitative, because they can only be classified into categories OD Quantitative, because they are measured on a naturally occuring numerical scale her the data are input as 1. 2. 3. 4. are they calitative or quantitative? O A Quantitative, because they we measured on a naturally occurring numerical sole Os Qualitative because they are more on a naturally occurring numerical scale OC Qualitative, because they cannot be meaningfully added subtracted, multiplied, or divided OD. Quantitative, because they cannot be meaningfully added, subtracted, multiplied, or divided
Quantitative data is data that is measured on a naturally occurring numerical scale.
This can be seen in the data input as 1, 2, 3, 4, which can be meaningfully added, subtracted, multiplied, or divided. Qualitative data, on the other hand, is data that cannot be meaningfully added, subtracted, multiplied, or divided. The data set consisting of classifications AB, C, and D is qualitative because it can only be classified into categories and cannot be meaningfully added, subtracted, multiplied, or divided. To illustrate this further, let’s take an example. If the categories are colours (A = Red, B = Blue, C = Green, and D = Yellow), the data set AB, C, and D cannot be meaningfully added, subtracted, multiplied, or divided, and therefore is qualitative.
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Write as a fraction in simplest form: 22%
Step-by-step explanation:
So 22% is 22% out of 100%
So
22/100
Now all you need is to simplify by dividing each side by 2
11/50
MTH115 – Principles of Mathematics
Assignment 4.2 – Technology 4
Recreate this table in a spreadsheet. Use built-in commands to find the column, row, and overall totals. After that, answer the given questions by using cell references in the spreadsheet. Round your answer to the whole percentage. Upload your sheet as an excel file.
Expenses
Rent Labor Supplies Total
Business 1 750 1300 2500
Business 2 1500 975 3600
Business 3 1200 850 1850
Business 4 450 1600 2900
Business 5 3200 5200 1000
Business 6 980 360 5600
Total
a. Labor makes up what percent of the total?
b. What percent of the total was Business 4's expenses?
c. Business 5's labor cost is what percent of the total labor expenses?
d. Supplies makes up what percent of Business 5's expenses?
Answer: I'm sorry, I am not able to create or upload spreadsheets in this platform due to recent restrictions. However, you can easily create this table in a spreadsheet program like Microsoft Excel and use built-in functions to find the desired information.
To answer the questions:
a. To find the percentage of the total that Labor makes up, you would divide the total Labor expenses by the overall Total expenses, then multiply by 100 to express the answer as a percentage.
b. To find the percentage of the total that Business 4's expenses make up, you would divide Business 4's Total expenses by the overall Total expenses, then multiply by 100 to express the answer as a percentage.
c. To find Business 5's labor cost as a percentage of the total labor expenses, you would divide Business 5's Labor expenses by the overall Labor expenses, then multiply by 100 to express the answer as a percentage.
d. To find the percentage of Business 5's expenses that Supplies make up, you would divide Business 5's Supplies expenses by Business 5's Total expenses, then multiply by 100 to express the answer as a percentage.
Step-by-step explanation:
taxi company a charges 4$ plus 0.5x per mile and taxi company b charges 5 $ plus 0.25x per mile
Graph it do they intersect?
Answer:
I have to submit the BRAINLIEST
pls mark as brainliest
will give brainliest. A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the slices of pie the college will need?
A. The college will have about 480 students who prefer pie.
B. The college will have about 640 students who prefer pie.
C. The college will have about 1,280 students who prefer pie.
D. The college will have about 1,440 students who prefer pie.
solve. |3x+2| = |2x-5|
Answer:
[tex]3x + 2 = 2x - 5 \\ 3x - 2x = - 5 - 2 \\ x = - 7[/tex]
Step-by-step explanation:
please make me as brainlest
Step-by-step explanation:
I hope it will help you...
johan reads that the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. how many kilograms is an average elephant's brain?
Answer:
your answer is also the solve
Answer:
m + 3.4 kilograms.
Step-by-step explanation:
Let's call the mass of an average man's brain "m" kilograms.
According to the information given, the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. This means that the mass of an average elephant's brain can be calculated as:
m + 3 4/10 = m + 3.4
So, the mass of an average elephant's brain is 3.4 kilograms greater than the mass of an average man's brain, which is m kilograms.
Therefore, the mass of an average elephant's brain is m + 3.4 kilograms.
help pls. Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.6 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
116.27 cubic inches
303.32 cubic inches
697.65 cubic inches
2,790.58 cubic inches
If Marshall met, but did not exceed, his goal, how many calls had he made in all after spending exactly 20 days making calls as a telemarketer? This is a arithmetic sequence SUM question. "In all" gives away that it's a "total" or "sum" question. Thus, you have to use the (20/2) × (24+119)= 1,430.
Marshall's total cost number of calls made after 20 days of telemarketing is 1,430, which is the sum of the sequence of 24 calls made on the first day and 119 calls made on the twentieth day.
Marshall has a goal of making 24 calls on the first day of telemarketing and increasing the number of calls by 5 each day for 20 days. This creates an arithmetic sequence which increases by 5 each day. The formula for the sum of an arithmetic sequence is (n/2) × (a + l), where n is the number of terms in the sequence, a is the first term and l is the last term. In this case, n = 20, a = 24, and l = 119. Plugging these values into the formula yields (20/2) × (24+119)= 1,430. This means that Marshall's total number of calls made after 20 days of telemarketing is 1,430, which is the sum of the sequence of 24 calls made on the first day and 119 calls made on the twentieth day.
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