a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
What is Domain?
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
What is Range?
The range of a function is the set of values that the function assumes.
What is Relation?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected
a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
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What is an equation of the line that passes through the point (−5,−2) and is parallel to the line x-y=5?
The required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the equation of the line will be:
The needed line will have the same slope as the parallel line.
The slope of the parallel line:
x - y = 5
y = x - 5
The parallel line's slope is 1.
Equation of a line with a slope of 1 through the point (-5,-2).
(y - y1) = m(x x1)
(y + 2) = 1(x + 5)
x - y + 3 = 0
Therefore, the required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.
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On the Set of axes below graph the line whose equation is 2y=-3x-2
The linear equation contains point (2,k).State the value of k.
The value of k in the point (2, k) which lies on the line is -4.
How to find the value of k?
Every point lying on the curve of the line satisfies the equation of curve. Therefore, substitute the point in the given equation of line to find the value of k.
According to the given question:
The given equation is: 2y = - 3x - 2.
This is written as: 3x + 2y + 2 = 0.
Given the point (2, k) lies on the line given.
That means it should satisfy the given equation.
So, to find the value of 'k', simply substitute the point on the line.
So, it becomes: 3(2) + 2(k) + 2 = 0
⇒ 6 + 2k + 2 = 0
⇒ 2k = - 8
Dividing by 2 throughout, we get: k = - 4
Hence, (2, -4) lies on the line.
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12. Electricity Company A charges 14 € per unit for the first 100 units in a quarter, and 11 % per unit after that. Electricity Company B charges a flat rate of $12 per unit. How many units must a customer use per quarter for Company A to be the cheaper option?
13 Taxi company A charges a minimum of $ 2.25 for each journey of up to 2 miles, plus per mile for every mile over that. Taxi company B has no minimum fare, but charges 95 per mile. Which of the following is the minimum number of miles over which taxi company A is cheaper than taxi company B ?
A 4
12. The customer should use 120 units in a quarter for company A to be cheaper.
What is cost management?
Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.
Solution:
Company A charges $14 for first 100 units = 14×100
= $1400
After that 11% of 14 = 1.54 per unit
Company B charges $12 per unit so for 100 units = $12×100
= $1200
For company A to be cheaper, customer must use 120 units of electricity from company B as expense for 120 units from company B will be $12×120 = $1440
and,
For 120 units of electricity from company A would be
$14×100 + 1.54×20 as after 100 units company A will charge 11%.
∴ for 120 units = 1400 + 30.8
= $1430.8
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13. For taxi company A to be cheaper customer must travel a minimum of 6 miles.
What is cost management?
Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.
Solution:
Given:
Company A charges $2.25 for a minimum of 2 miles journey and after that 85 cents per mile.
Company B charges 95 cents per mile without any minimum mile condition.
Let's assume
no. of miles = 4
fare from A = $2.25(2 miles) + 85 cents(1 mile) + 85 cents(1 mile)
= $3.95
fare from B = 95 cents × no. of miles
= 95 cents × 4
= $3.8
∵ Fare of company A is greater than B, minimum number of miles should be greater than 4.
now,
Let's assume
no. of miles = 5
fare from A = $2.25 + 85 cents + 85 cents + 85 cents
= $4.8
fare from B = 95 cents × no. of miles
= 95 cents × 5
= $4.75
∵ Fare of company A is greater than B minimum number of miles should be greater than 5.
now,
Let's assume
no. of miles = 6
fare from A = $2.25 + 85 cents + 85 cents + 85 cents + 85 cents
= $5.65
fare from B = 95 cents × no. of miles
= 95 cents × 6
= $5.7
∵ Fare of company A is less than B.
∴ Minimum number of miles should be 6.
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The diameter of a circle is 18m.Eugene claims that the circumference of the circle is about 113.04m.
Answer:
formula. for circumference of a circle is. : 2πR. if you have the radius.
As the diameter is twice the radius, then circumference is. diameter π
then : 18*π≈ 56.52
the mistake was to take the diameter as the radius.
Step-by-step explanation:
check answer
6 divided by 0.528 long division (answer QUICKLY)
Answer: 11.36
Step-by-step explanation:
↓ Please look in the screenshot below...
On July , the billing date, Marvin Zug had a balance due of $265.72 on his credit card. His card charges an interest rate of 1.25% per month. The transactions he made are to the right.
a) Find the finance charge on August , using the previous balance method.
b) Find the new balance on August 7.
(see photo)
Answer:
475$
Step-by-step explanation:
If pentagon OPQRS is dilated by a scale factor of from the origin to create O′P′Q′R′S′, what is the ordered pair of point S′?
(8.75, 5.25)
(1.25, 0.75)
(1.75, 3.5)
(3.5, 8.75)
The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).
What is scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’
Multiply the coordinates of point P by the scale factor 7/4 to get the coordinates of P'.
Given : P(-5,3)
P' (x,y) = P (-5 x 7/4 , 3 x 7/4)
= P(-8.75, 5.25)
Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).
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3) Solve. Answer needs to remain as an improper
fraction.
3/4 - 3 1/2 + 6
Answer:
Exact form: 13/4
Decimal form: 3.25
Mixed form: 3 1/4
Step-by-step explanation:
The 11 students in the Environmental Club represent 2% of the students in the seventh grade. How many students are in the seventh grade?
Answer:
The number of students in the seventh grade is 550.
Step-by-step explanation:
To find the number of students in the seventh grade, we need to use the information given in the problem: the number of students in the Environmental Club (11 students) and the percentage of students in the seventh grade that the Environmental Club represents (2%).
We can set up an equation to represent this information:
11 students / 2% = X students / 100%
The left side of the equation represents the number of students in the Environmental Club and the percentage of the seventh grade that they represent. The right side of the equation represents the total number of students in the seventh grade and the percentage that represents the whole.
Since percentages are just fractions with a denominator of 100, we can rewrite the equation as:
11 students / 0.02 = X students / 1
Then, we can use algebraic techniques to solve for X. One way to do this is to cross-multiply:
X = (11 students * 1) / 0.02
= 550 students
Therefore, there are 550 students in the seventh grade.
Solve F = MGH for H. G=?
The value of G = F/MH for H
What is expression ?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent all of the numerical constants, variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
According to the given information
F = MGH
we need to find the value for G
Dividing the above equation by MH
F/MH = MGH/MH
SO
G = [tex]\frac{F}{MH}[/tex]
So the value of G = F/MH for H
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A ball is thrown from an initial height of 4 feet with an initial upward velocity of 18/fts. The ball's height h (in feet) after t seconds is given by the following.
=h+4−18t16t2
Find all values of t for which the ball's height is 8 feet.
All values of t for which the ball's height is 8 feet are 0.82 or 0.305.
What is quadratic equation?
Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.
Main Body:
The actual equation is
h= 4- 18t +16t²
initial height of ball = 4 ft
The problem asks for a time when the ball's height will be 8 ft. To find these times, I plug 8 in for h and solve for t:
8 = 4+18t -16t²
16t² - 18t +4 =0
Using the quadratic equation:
t = {18 ±√((18)² - 4*16 *4 )}/2*16
t = 18 ± √(324 - 256)/32
t = (18 ± √68) /32
t = (18±8.24)/32
t = 0.82 or 0.305
Hence ,all values of t for which the ball's height is 8 feet are 0.82 or 0.305.
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16. Find the angle between 0 and 2π coterminal with the angle
23π/3
The angle between 0 and 2π coterminal with the angle 23π/3 will be equal to 17π/3.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the angle between 0 and 2π coterminal with the angle 23π/3. The coterminal angle will be calculated as,
To calculate the coterminal angle subtract 2π from 23π/3. Solve mathematically,
Coternimal = ( 23π / 3 ) - 2π
Coterminal = 9 23π - 6π ) / 3
Coterminal = 17π / 3
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somebody please help!!
Step-by-step explanation:
I just answered this with all explanations.
the 2 solutions are
x = 6
x = -12
I need help quick please
Answer:
x is (2,0) and y is (0, -2)
Step-by-step explanation:
Hope this helps
raise the fraction to higher terms as indicated. 2/3 to twenty-fourths
Answer:
16/24
Step-by-step explanation:
To raise a fraction, we have to multiply by 24/3, which is 8:
2 * 8 / 3 * 8 =
16/24
A tree is 12 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet.
Answer:
The tree is 396 feets height
Step-by-step explanation:
1 m = 3.3 ft
then
12 meters to feet is:
(12)*(3.3) = 396
Finding slope given the graph of a line on a grid
Find the slope of the line graphed below.
3. Write the equation Passing through ( -5, 2) with a slope of 3
Answer:
y = 3x + 17
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 )
here m = 3 , then
y = 3x + c ← is the partial equation
to find c substitute (- 5, 2) , that is x = - 5, y = 2 into the partial equation
2 = - 15 + c ⇒ c = 2 + 15 = 17
y = 3x + 17 ← equation of line
please help with this it is very important its a final
At the July 1980 Olympics, the record for the women's shot put was 22.41 meters, which was 5.09 meters less than double the 1948 Olympic winning distance. What was the women's winning shot put distance in the 1948 Olympics?
100 square floor tiles with sides 1 foot long
What was the length of each side of the room?
Answer: 100 feet
Step-by-step explanation:
If there are 100 square floor tiles, and each side is one foot long, we will multiply the number of tiles by the length of each tile to find the length of each side of the room.
100 tiles * 1 foot length = 100 feet
The graph of a line y = 2x -1 is shown below. Find the Slope and y-intercept of the function.
Answer:
Slope = 2
y-intercept = -1
Step-by-step explanation:
In the slope-intercept form of the equation of a line (y=mx+b), m equals the slope and b represents the y-intercept.
So, for this problem, m=2 and b=-1. This means the slope is 2 and the y-intercept is -1.
To order the right amount of flooring, you need to know the floor area of the living room
hown below. What is that area, in square feet?
Answer: Length (in feet) x width (in feet) = area in sq. ft.
Step-by-step explanation:
What is C ?
⁸ ⁶
A. 10
B. 28
C. 35
D. 14
Answer:
B
Step-by-step explanation:
assuming you mean [tex]8C_{6}[/tex]
using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) × 3 × 2 × 1
then
8[tex]C_{6}[/tex]
= [tex]\frac{8!}{6!(8-6)!}[/tex]
= [tex]\frac{8!}{6!(2!)}[/tex]
= (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (6 × 5 × 4 × 3 × 2 × 1 × 2 × 1
cancel (6 × 5 × 4 × 3 × 2 × 1 ) on numerator / denominator
= (8 × 7 ) / 2 × 1
= 56 ÷ 2
= 28
Apologies for formatting.
Multiple choice: Select the best answer for Exercises 49 to 52. Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (a) 0.008. (b) 0.02. (c) 0.03. (d) 0.04. (e) 0.208.
The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04
The margin of error is a statistic that describes how much random sampling error there is in survey results.
Given in question,
n = 400
p = 317/400
= 0.7925
Confidence Level = 95%
= 0.95
Formula for margin error, E = [tex]z\sqrt{\frac{p(1-p)}{n} }[/tex]
Confidence level corresponding to 95 % confidence interval, z = 1.96
Therefore,
Margin Error, E = [tex]1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }[/tex]
= 0.0397
≈ 0.04
Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.
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If the volume of a cone is 847picm³ and the height is 7 cm, what is the radius?
r≈10.75cm
Answer:
r≈10.75cm
V=πr^2h/3
Tamala’s school day is 7 1/2 hours. She has six classes that are 7/6 of an hour long each. How many hours is Tamala not in class while she is at school?
Answer:
The correct answer is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
If she has 6 classes, then the total hours of classes are:
[tex]\frac{6}{1}[/tex] · [tex]\frac{7}{6}[/tex] = [tex]7[/tex]
[tex]7[/tex] · [tex]\frac{1}{2}[/tex] - [tex]7[/tex] = [tex]\frac{1}{2}[/tex]
On a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 20. Find the z-score of a person who scored 115 on the exam.
The value of z-score of a person who scored 115 on the exam will be;
⇒ z - score = - 1
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The scores are normally distributed with a mean of 135 and a standard deviation of 20.
Now,
Since, The scores are normally distributed with a mean of 135 and a standard deviation of 20.
We know that;
⇒ z - score = X - μ / σ
Substitute all the values, we get;
⇒ z - score = 115 - 135 / 20
⇒ z - score = - 20/20
⇒ z - score = - 1
Thus, The value of z-score of a person who scored 115 on the exam will be;
⇒ z - score = - 1
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Al, Bill, Dill, and Will ate some apples. Each of them ate a different
number of apples, and each of them ate at least two apples. However,
their father ate even more than they ate together; he ate 15. (Maybe
they were rather small apples!)
Could one of the boys have eaten more than five apples?
Answer:
Yes
Step-by-step explanation:
let x = one boy
let y = another boy
let z = a third boy
x + 2 + y + 2 + z + 2 = 15 Combine like terms
6 + x + y + z = 15 Subtract 6 apples from both sides
x + y + x = 9
When we subtract out the 2 apples each brother know that they ate at lease 2 apples each we are left with a total of 9 apples.
One boy could have eaten 4 additional apples? Yes.
4 + 1 + 1 < 9
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $96Two adults and three children must pay $68 Find the price of the adult's ticket and the price of a child's ticket.
After solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, 2 equations can be formed:
Let a be adults and c be children.
3a + 4c = 96 ...(1)
2a + 3c = 68 ...(2)
Now, take equation (1):
3a + 4c = 96
3a = 96 - 4c
a = 96 - 4c/3
Now, substitute a = 96 - 4c/3 in equation (2):
2a + 3c = 68
2(96 - 4c/3) + 3c = 68
96 - 4c/3 + 3c = 68/2
96 - 4c + 3c = 34*3
-c = 102 - 96
c = $6
Now, substitute c = 6 in equation (1):
3a + 4c = 96
3a + 4(6) = 96
3a + 24 = 96
3a = 96 - 24
3a = 72
a = 72/3
a = $24
Therefore, after solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.
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