Addie's income by running a sandwich delivery service is given by the function y = 12x + 5, which has a domain and range of [0 , +∞) and [5 , +∞), respectively.
In mathematics, a function is the representation of the relationship of a set of input(X) and its corresponding output(Y). The set of x is called the domain while the set of the corresponding y is the range.
If Addie runs a sandwich delivery service. her income can be measured using the function
y = 12x + 5
where x = number of sandwiches she delivers
y = income
The domain of a function is the set of values that we are allowed to plug into our function. The domain of any function of x is always the set of all real numbers but, reasonably speaking, we must consider the situation given. The number of sandwiches she delivers can only range from 0 to positive infinity, not negative.
domain : {x | x ≥ 0} or [0 , +∞)
On the other hand, the range of a function is the set of values of the function after plugging in the value of x.
Substituting our domain [0 , +∞) in the function.
y = 12x + 5
y = 12(0) + 5
y = 5
y = 12(+∞) + 5
y = +∞
range : {y | y ≥ 5} or [5 , +∞)
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Solve the inequality. Graph the solution -3s<11s+1
[tex]-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}[/tex]
===========================
[tex]\textcopyright ELIZA[/tex]
Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 3,6,12,24,48, .......
The next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
According to the given question.
We have a sequence 3, 6, 12, 24, 48, ..
Since, the first term of the sequence is 3.
The second term of the sequence is 6.
The third term of the sequence is 12.
Here, we can say that the next term is twice the previous term.
So, the next two terms of the given sequence, i.e.
Sixth term = 48 × 2 = 96
Seventh term = 96 × 192
Therefore, the formula for the nth term of the sequence is given by
[tex]T_{n+1} = 2T_{n}[/tex].
Hence, the next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
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Julian is trying to decide on a future career. He has narrowed down his choices to orthodontist, sound engineering technician, police officer, or editor. The following table represents the total employment numbers for 2006 and projected employment numbers for 2016.
Orthodontist
Sound engineer technician
Police officer
Editor
2006
9,206
16,125
648,982
122,273
2016
10,214
17,864
719,041
124,135
Which profession is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016?
a.
Orthodontist
b.
Sound engineer technician
c.
Police officer
d.
Editor
The profession that is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016 is B. sound engineer technician.
How to calculate the percentage?The increase in percentage for orthodontist will be:
= (10214 - 9206) / 9206 × 100
= 1008 / 9206 × 100
= 10.95%
The increase in percentage for sound engineer will be:
= (17864 - 16125) / 16125 × 100
= 1739/16125 × 100
= 10.79%
The increase in percentage for police officer will be:
= (719041 - 648982) / 719041 × 100
= 70059/719041 × 100
= 9.74%
The increase in percentage for editor will be:
= (124135 - 122273)/124135 × 100
= 1862/124135 × 100
= 1.5%
Therefore, the sound engineer has the greatest percentage increase.
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Answer:
sound engineer
Step-by-step explanation:
Solve each system.
(1/2)x + (2/3)y= 1 , (3/4)x - (1/3)y = 2
The solution of the given system of equations is (3//2, -3/8)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
(1/2)x + (2/3)y= 1 ......... (1)
(3/4)x - (1/3)y = 2 ..........(2)
Multiply equation (1) by 6
3x + 4y = 6 ..... (3)
Multiply equation (2) by 12
9x - 4y = 24 ...... (4)
Add equation (3) and (4)
3x + 4y = 6
9x - 4y = 24 +
12x = 30
x = 30/12 = 5/2
Substitute x = 5/2 into equation (3)
3x + 4y = 6
3. (5/2) + 4y = 6
15/2 +4y = 6
4y = (12 - 15)/2 = -3/2
y = -3/8
The solution is (3/2, -3/8)
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given: ∆abc with vertices a(-3,0), b(0,6), and c(4,6) Find the equations of the three perpendicular bisectors in abc.
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
What are the equations of the perpendicular bisectors of the triangle ABC?
Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.
First, determine the midpoints of each side:
Side AB
M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)
M₁(x, y) = (- 1.5, 0) + (0, 3)
M₁(x, y) = (- 1.5, 3)
Side BC
M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)
M₂(x, y) = (0, 3) + (2, 3)
M₂(x, y) = (2, 6)
Side AC
M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)
M₃(x, y) = (- 1.5, 0) + (2, 3)
M₃(x, y) = (0.5, 3)
Second, determine the slope of the perpendicular bisectors:
Side AB
m = (6 - 0) / [0 - (- 3)]
m = 2
m' = - 1 / m
m' = - 1 / 2
Side BC
m = (6 - 6) / (4 - 0)
m = 0
m' = - 1 / m
m' = NaN (Vertical line)
Side AC
m = [4 - (-3)] / (6 - 0)
m = 7 / 6
m' = - 1 / (7 / 6)
m' = - 6 / 7
Third, derive the equations of the bisectors:
Side AB
b = 3 - (- 1 / 2) · (- 1.5)
b = 9 / 4
y = - (1 / 2) · x + 9 / 4
Side BC
x = 2
Side AC
b = 3 - (- 6 / 7) · (0.5)
b = 24 / 7
y = - (6 / 7) · x + 24 / 7
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
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Alan deposits $10 per month into his savings account. Which expression could represent the amount he saves, in dollars, in y years?
Answer:
in 1 year Allan would save 120 dollars, this is because, 10x12=120
Step-by-step explanation:
to find out what he would save I 2 years just multiply 120 by 2, 120x2=240, and for 3 years multiply 120 by 3, and so on.
im stuck on this problem and i need help. oh also make sure that your answer is completely right
Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y ' = y 2xy, y(2) = 1. (round the answer to four decimal places.) y(2.5) =
y(2.5) = 15.9389 is Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem.
What is euler's method?
First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.
f(x,y) = 3y+2xy
So, starting at t0 = 2, repeat the above sequence until t0>2.5
a) m = f(2,1) = 3(1)+2(2)(1) = 7
b) y1 = y0 + hm = 1+0.1(7) = 1.7
c) t1 = t0 + h = 2.1
d) show t1 and y1
e) t0 = t1 = 2.1
f) y0 = y1 = 1.7
2nd iteration
a) m = f(2.1,1.7) = 3(1.7)+2(2.1)(1.7) = 5.1 + 7.14 = 12.24
b) y1 = y0 + hm = 1.7+0.1(12.24) = 1.7 + 1.224 = 2.924
c) t1 = t0 + h = 2.2
d) show t1 and y1
e) t0 = t1 = 2.2
f) y0 = y1 = 2.924
This is what I got for all iterations from a simple program x y
2.1 1.7
2.2 2.924
2.3 5.08776
2.4 8.9544576
2.5 15.938934528
y(2.5) = 15.9389
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need help w this please
A pair of parametric equations is given. x = 2t, y = t 5 (a) sketch the curve represented by the parametric equations. use arrows to indicate the direction of the curve as t increases.
Refer to the image attached.
What are parametric equations?Parametric equation uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used.
Now,
In order to plot the graphs of the given parametric equations, we will be sketching a table, in which, the values of the equations will be found at various values of the parameter.
=> Refer to the table in the image attached.
For the values so found of the parametric equations for the respective parameter, a graph will be plotted for both the equations:
Refer to the graph in the image attached.
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prove that the sum of the squares of two consecutive even numbers is a multiple of 4
Answer:
Since the final answer has a factor of 4, it is a multiple of 4.
Step-by-step explanation:
Let the smaller even number be 2n.
The next greater even number is 2n + 2.
(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)
A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
c. What is the probability that the first chip is green and the second is brown?
The probability that the first chip is green and the second is brown is 1/20,
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting the chip is green;
= 5/20
= 1/4
The probability of selecting the chip is brown;
= 4/20
= 1/5
Then the probability that the first chip is green and the second is brown
= 1/4 x 1/5
= 1/20
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What is the mean of 3, -10, -2, 13, 11
Answer:
= (3 + -10 + -2 + 13 + 11) / 5
= 15/5
Step-by-step explanation:
3
Hey there!
Your mean simply means, your average….
To find it you have to ADD all of your numbers and DIVIDE it by the total number you have in your data plot.
3 + -10 + -2 + 13 + 11 / 5
= 3 - 10 - 2 + 13 + 11 / 5
= -7 - 2 + 13 + 11 / 5
= -9 + 13 + 11 / 5
= 4 + 11 / 5
= 15 / 5
= 3
Therefore, your answer should be: 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 2,100 people entered the park, and the admission fees that were collected totaled $4,900. How many children and how many adults were admitted?
From the calculation carried out below, the number of children admitted was 1,400 and the number of adults admitted was 700.
How do we calculate the different numbers of people admitted?
This question can be solved using the substitution method as follows:
x = Number of children admitted
y = Number of adults admitted
x + y = 2,100 ............................................. (1)
1.50x + 4y = 4,900 ................................ (2)
From equation (1), we have:
x = 2,100 - y ................................................. (3)
Substituting x = 2,100 - y into equation (2) and solving for y, we have:
1.50(2,100 - y) + 4y = 4,900
3,150 - 1.50y + 4y = 4,900
2.50y = 4,900 - 3,150
2.50y = 1,750
y = 1,750 / 2.50
y = 700
Substituting y = 700 into equation (3), we have:
x = 2,100 - 700
x = 1,400
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the question is shown in the picture
Answer:
Final Cost of 3 pounds: 7.25
Final cost of p pounds: 3.50p
Step-by-step explanation:
3.50p - 3.25 = ?
3.50(3) - 3.25 = ?
10.50 - 3.25 = $7.25
Write an expression of the cost to buy at least one pound of chicken.
3.50p
I hope this helps!
please help me with this geometry question
Answer:
-t*(t -16) ≥ 39
-t*(t -16) = 39
t = 3 or 13 hours
Step-by-step explanation:
When number of people is at 39 or more means the number of people of greater than or equal to 39.
So, the inequality is,
-t*(t -16) ≥ 39
When the number of people is 39, the equation is,
-t*(t - 16) = 39
-t²+ 16t = 39
0 = 39 + t² - 16t
t² - 16t + 39 = 0
Sum = -16
Product = 39
Factors = -3 , -13 [ (-3) * (-13) = 39 & (-3) +(-13) = -16 ]
Rewrite the middle term using the factors.
t² - 3t - 13t + 39 = 0
t(t -3) - 13(t - 3) = 0
(t -3)( t - 13) = 0
t -3 = 0 ; t- 13 = 0
t = 3 or t = 13
t = 3 hours or 13 hours.
I need help in those questions please
The other root of the given quadratic equation is a = ± 3/√2.
Given that, x=2 and x²+ax+12=0.
What are the roots of quadratic equations?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Now, put x=2 in x²+ax+12=0 and find the value of a.
That is, 2²+2a+12=0
⇒4+12+2a=0
⇒16+2a=0
⇒2a=-16
⇒a=-8
So, the value of a is -8.
Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.
That is, 6=2(0)²+b(0)+c
⇒ c=6
6=2(4)²+b(4)+c
⇒ 6 = 32+4b+c
⇒ -26 = 4b + 6
⇒ 4b = -32
⇒ b = -8
So, the value of b is -8 and the value of c is 6.
Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.
That is, 2a²+a/a -9 = 0
⇒ 2a² - 9 = 0
⇒ a²=9/2
⇒ a = ± 3/√2
Therefore, the other root of the given quadratic equation is a = ± 3/√2.
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Use the Distributive Property to rewrite and evaluate 8.598 by filling in the blanks below.
8-598 = 8(600- __)
=
8 (600) - 8(__)
= 4800 - __
= __
Answer:
4784.
Step-by-step explanation:
8 * 598 = 8(600- _2_)
=
8 (600) - 8(_2_)
= 4800 - _16_
= 4784__
A spinner contains the numbers 1 through 80. what is the probability that the spinner will land on a number that is not a multiple of 11?
The probability that the spinner will land on a number that is not a multiple of 11 is 73/80.
What is probability ?Multiples of 11 are 11,22,33,44,55,66,77.
That means there are 7 multiples of 11
80 -7 = 73
There are 73 non multiples of 11
P( non multiples of 8) = non multiples of 11 / total
= 73/80
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. By employing it, we are only able to forecast the likelihood of an event, or how likely it is, to occur.
According to the probability formula, the likelihood of an event occurring, or P(E), is determined by the proportion of positive outcomes to all other outcomes.
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Hello! Please help me with this. I'm very desperate lol. Its 16. Ill give brainliest
Answer:
You showed the right work and got the right answer!
x = 6
Step-by-step explanation:
Since B is in the middle of A and C, AB + BC = AC
So,
2x - 11 + 8 = x + 3
x - 3 = 3
x = 6
In a bag of gum balls 30% are blue. There are 21 blue gum balls in the ball how many gum balls are there in all
Answer:
70
Step-by-step explanation:
21 is 30 % so multiply 21 by 3 which is 63 and then divide 21 by 3 which is 7 and add the 7 to 63
PLEASE HELP ME WITH THIS!!!!
Please help!:)))))))))))
Answer:
one way to name the symbol is our and another way to name the symbol is rco
please help with this question and determine a,b,c,d and e
Answer:
a=7
b=8
c=12
d=33
find e by adding up all numbers in the Venn diagram then subtract the total amount of people by total from the Venn diagram to find e
A new community sports vs complex is being built in Erie. the perimeter of the rectangular playing field is 232 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
The dimensions of the rectangular playing field are:
length = 92 yards and
width = 24 yards.
Given, the perimeter of the rectangular field is : 232 yards.
From the given question, length of the field is 4 yards less than quadruple the width.
hence, let the width of the field be x yards.
Length of the field = 4x - 4 yards.
we know that perimeter of the rectangle = 2(l+w)
therefore, substitute the values in the above formula:
2(4x - 4 + x) = 232
2(5x - 4) = 232
multiply the terms.
10x - 8 = 232
arrange the constants on one side.
10x = 232 + 8
10x = 240
x = 240/10
x = 24
hence we get the width as x = 24 yards.
Now substitute the value of x to find out the value of the length.
therefore, l = 4x - 4
l = 4(24) - 4
l = 96 - 4
l = 92
Therefore length and width of the rectangular field is 92 and 24 yards respectively.
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whta slope line goes through (4,5) &(-1,-5)
Answer:
y = 2x - 3
Step-by-step explanation:
1) Find the slope
The slope of any function, if given the coordinates of at least two of the points it crosses, is given by the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
We are given the points (4, 5) and (-1, -5), therefore, we can substitute their values:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-1)} = \frac{10}5 = 2[/tex]
2) Find the line's equation
We can find the line's equation by substituting one of the given points and the slope we just found into the formula [tex]y - y_1 = m(x - x_1)[/tex]:
[tex]y - 5 = 2(x - 4) \\ \to y - 5 = 2x - 8 \\ \to y = 2x - 3[/tex]
Answer: 2x - 3.
Step-by-step explanation: I took the test.
Write an equation in slope-intercept form for the line that has a slope of -5 and passes through the point (-3, -8).
Answer:
[tex]y = -5x - 23[/tex]
Step-by-step explanation:
To write an equation in the slope-intercept form for a line, given the coordinates of a point on the line as well as the line's slope, we use the following formula:
[tex]\boxed{y - y_1 = m(x - x_1)}[/tex],
where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] are the given coordinates of a point.
In this question, we are told that the slope is -5 and the coordinates of a point passing through the point are (-3, -8).
Therefore, using the above formula, we can write:
[tex]y - (-8) = -5(x - (-3))[/tex]
⇒ [tex]y + 8 = -5(x + 3)[/tex]
⇒ [tex]y + 8 = -5x - 15[/tex] [Distributing -5 into the brackets]
⇒ [tex]y = -5x - 15 - 8[/tex] [Subtracting 8 from both sides]
⇒ [tex]y = -5x - 23[/tex]
This means that the equation for the slope-intercept form of the line is [tex]y = -5x - 23[/tex] .
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ = 1, r=0.5
The explicit formula for the given sequence is a(n) = 2 . (0.5)ⁿ and the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
Given the parameters:
First term, a(1) = 1, and
common ratio, r = 0.5
We are ask to find the explicit formula for the geometric sequence and generate the first five terms.
Recall that in a geometric sequence:
a(n) = a(1) . rⁿ⁻¹
Where a(n) is the nth term.
Substituting a(1) = 1 and r = 0.5:
a(n) = 1 . (0.5)ⁿ⁻¹
= (0.5)⁻¹. (0.5)ⁿ
= 2 . (0.5)ⁿ
To generate the first five terms, we can use the above explicit formula for n = 1, 2, ..., 5 or we can use a recursive procedure. Remember that in a geometric sequence:
a(n) = a(n-1) . r
Therefore,
a(1) = 1 (given)
a(2) = 1 . (0.5) = 0.5
a(3) = 0.5 . (0.5) = 0.25
a(4) = 0.25 . (0.5) = 0.125
a(5) = 0.125 . (0.5) = 0.0625
Thus, the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
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A store sells a water blaster for $26. They bought it for $20. What is the markup percent?
The markup percent of the water blaster in the store is 30%
How to calculate the markup percent of the water blaster ?The store sells a water blaster for $26
They bought it for $20
New price is $26
Original price is $20
The markup percent can be calculated as follows
26-20/20 × 100
= 6/20 × 100
= 0.3 × 100
= 30%
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98!/100! x 10 (! = the number times every number before it and it) ex: 4! = 1 x 2 x 3 x 4
The value of the factorial expression is 99/10
How to evaluate the factorial expression?The expression is given as
98!/100! x 10
The above expression implies that we multiply 10 by the quotient of 98! and 100!
This can be done directly using a calculator, and it can be solved step by step
The step by step procedure is as follows
Expand the denominator
98!/100! x 10 = 98!/100 * 99 * 98! x 10
Evaluate the quotient
98!/100! x 10 = 1/100 * 99 x 10
This gives
98!/100! x 10 = 1/10 * 99
Evaluate the product
98!/100! x 10 = 99/10
Hence, the value of the factorial expression is 99/10
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