I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
Answers
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
Related Questions
7. A crew of electricians can wire 6 houses in 243 hours. How many hours will it take them to wire
13 houses?
Answers
243*2=486
243/6=40.5 Or how many hour it would take to wire one house.
486+40.5=526.5Hrs
PLEASE HELP
ILL GIVE BRAINLIEST
Answers
Answer:
f(7x−1)=63x−16
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
since f(x) and g(x) are equal, we can make the equation, 9x-7 = 7x - 1
9x = 7x + 6, 2x = 6, x = 3
what is 2 times 4 time 2
Answers
Answer:
16
Step-by-step explanation:
Answer:
16
Explanation:
2 x 4 = 8
8 x 2 = 16
suppose that the life distribution of an item has the hazard rate function of what is the probability that
Answers
Answer:
that what
Step-by-step explanation:
if you subtract 19 from my number and multiply the difference by -2, the result is -8
Answers
Answer:cool
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
let the number be 'a'
-2(a - 19)= -8
open the brackets
-2a + 38 = -8
collect like terms
38 + 8 = 2a
46 = 2a
a = 23
What is the slope of a line that is perpendicular to the line y =-1/5
Answers
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 0 0 . All lines that are parallel to y=−15 y = - 1 5 have the same slope of 0 .
Tickets for a drumline competition cost $5 at the gate and $3 in advance. One hundred more tickets were sold in advance than at the gate. The total revenue from ticket sales was $1990. How many tickets were sold in advance?
Answers
Answer:
The number of tickets sold at the gate is [tex] G = 211.25[/tex]
The number of tickets sold in advance is [tex] A = 311.25 [/tex]
Step-by-step explanation:
From the question we are told that
The cost of a tickets at the gate is [tex]a = \$ 5[/tex]
The cost of a ticket in advance is [tex]b = \$ 3[/tex]
Let the number of ticket sold in the gate be G
Let the number of ticket sold in advance be A
From the question we are told that
One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as
[tex]G + 100 = A[/tex]
From the question we are told that
The total revenue from ticket sales was $1990 and this can be mathematically represented as
[tex]5 G + 3A = 1990[/tex]
substituting for A in the equation above
[tex]5 G + 3[G + 100]= 1990[/tex]
[tex]5 G + 3G + 300= 1990[/tex]
[tex] 8G + 300= 1990[/tex]
[tex] 8G = 1690[/tex]
=> [tex] G = 211.25[/tex]
Substituting this for G in the above equation
[tex]5 [211.25] + 3A = 1990[/tex]
=> [tex] 3A = 1990 - 1056.25[/tex]
=> [tex] A = 311.25 [/tex]
PLEASE HELP ME ANSWER BOTH QUESTIONS WILL MARK BRAINLIEST!!!
Answers
Answer:
2034
Step-by-step explanation:
(9x+5)+(-2x^2+10x)
(9x+5)+(−2x
2
+10x)
Answers
Answer:
If i´m correct and read the answer correct it should be:
-18x³+80x²+65x+5
Step-by-step explanation:
Hopefully this is correct, I couldn't understand if (-2x 2+10x) was spaced or if it was being multiplied.
Solve -2(2x + 5) - 3 = -3(x - 1).
Answers
The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.
What is distributive property?Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.
-2(2x + 5) - 3 = -3(x - 1)
To solve this equation, we need to first use the distributive property to expand the left side of the equation.
We have:
-4x-10-3 = -3(x - 1)
-4x-13 = -3(x - 1)
Now, we can group the like terms on the left side and the right side of the equation.
On the left side, we have -4x - 13 and on the right side, we have -3x + 3.
-4x-13 = -3x + 3
To solve for x, we can add 3x to left side of the equation and add 13 to the right side.
This results in the equation:
-4x+ 3x = 13 + 3
Now, we can add 3x with -4x of the equation to isolate the x-term.
We have:
-x = 16
x = - 16
For more questions related to equation
https://brainly.com/question/17145398
#SPJ1
Order from least to greatest:
-5/6,0.567,-0.11,-1/4
Answers
Answer:
-5/6,-1/4,-0.11,0.567
Step-by-step explanation:
if angle 4 equals 50 degrees find the measure of angle 5 will mark brainiest
Answers
Answer:
∠5 = 50°Step-by-step explanation:
its alternate internal angles:
∠4 ≅ ∠5 (angle 4 is congruent or equal to alternate internal angle)
therefore,
∠5 = 50°
The measure of angle 5 should be considered as the 50 degrees when angle 4 should be equivalent to 50 degrees.
What is alternate internal angles?Alternate interior angles should be created via intersecting the 2 parallel lines in a transversal way. It should be located that lies between the two parallel lines.
Since the given diagram shows the alternate internal angles
Since angle 4 is 50
So angle 4 should be congruent or equivalent to alternate internal angle)
So angle 5 should be 50 degrees.
learn more about an angle here: https://brainly.com/question/21103473
What is the absolute value of 5,234?
Answers
Answer:
Step-by-step explanation:
5.234
Find the unknown angle measures.
Answers
Answer:
x = 9°
y = 119°
Step-by-step explanation:
Given,
y° = 61°+58° { the exterior angle formed by producing the side of triangle is equal to two non-adjacent angle}
or, y° = 119°
therefore, y° = 119°
Now,
52°+y°+x° = 180°{the sum of angle if triangle is 180°}
or, 52°+119°+x°= 180°
or, 171°+x° = 180°
or, x° = 180°-171°
or, x° = 9°
therefore, x° = 9°
Which of the expressions below will have a 8 in the thousandths place of the quotient? Select all that apply.
A) 765.812 ÷ 100
B) 98.14 ÷ 1,000
C) 18.723 ÷ 100
D) 22.38 ÷ 10
Answers
Answer:
A
Step-by-step explanation:
What formula is used to
determine the expected value for a variable?
Answers
Find the measure of the missing angle
Answers
Answer:
M1=108° M2=72°
Step-by-step explanation:
M1 and the original 108° angle are equal, and to calculate M2, which is on the same straight line as the original 108°, we must remember that all angles on a straight line add up to 180°. So, 180-108=72, making M2 72°
PLEASE HELP Please i don’t understand
Answers
Answer:
answer is 5
Step-by-step explanation:
f(5)= -5×5^2+26×5
= -125+130
= 5
Question 3 of 6 (1 point) Attempt 33 of Unlimited View question in a popup
2.4 Section Exercise 6
In a study of 550 meals served at 75 campus cafeterias, 77 had less than 10 grams of fat but not less than 350 calories; 81 had
less than 350 calories but not less than 10 grams of fat; 186 had over 350 calories and over 10 grams of fat.
Part: 0/2
E
Part 1 of 2
(a) What percentage of meals had less than 10 grams of fat? Round your answer to the nearest tenth of a percent.
of the meals studied, 1% of them had less than 10 grams of fat.
Answers
Answer:
10%
Step-by-step explanation:
(a) What percentage of meals had less than 10 grams of fat?
(b) Round your answer to the nearest tenth of a percent.
To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.
(A) Total number of meals = 550
Number of meals having less than 10 grams of fat = 77
Percentage of meals having less than 10 grams of fat = 77/550 × 100
= 0.14 × 100 = 14%
(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').
The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%
A lumber supplier sells 96-inch pieces of oak. Each piece must be within ¼ of an inch of 96 inches. Write and solve an inequality to show acceptable lengths.
Answers
Answer:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
Step-by-step explanation:
Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.
This situation can be represented by the following absolute value inequality:
[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].
The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.
To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.
First apply the rule |x| = y → x = [tex]\pm[/tex]y
|x-96| = 1/4
x - 96 = [tex]\pm[/tex]1/4
x = [tex]96 \pm 1/4[/tex]
(These are just the minimum, and maximum sizes)
Now with a less than or equal to, the solutions are now everything included between these two values.
Therefore:
[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]
With less than inequalities, you must have the lower value on the left, and the higher value on the right.
If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.
please answer this The cost of 2.5 pounds of cheese is $5.60.
D. How could you find the cost for 5 pounds of cheese without finding the cost per pound? Type your answer in the box.
Answers
Answer:
$11.20
Step-by-step explanation:
you just double the cost of 2.5 pounds because 2.5 +2.5 is 5
Answer:20.16
Step-by-step explanation:
That is we want the price of
9
pounds (lets call it
$
x
) to be such that
$
5.60
:
2.5
pounds
is the same as
$
x
:
9
pounds
or written as fractions, we want
$
5.60
2.5
pounds
=
$
x
9
pounds
That is
XXX
$
x
=
$
5.60
2.5
pounds
×
9
pounds
XXXXX
=
$
50.40
2.5
=
$
20.16
Kari is building a rectangular garden bed. The length is 6 feet. She has 20 feet of boards to make the sides. Write and solve an inequality to find the possible width of her garden bed.
Answers
Answer:
ahe using 12 feet of boards and threre 8 ft of board left so i guess the with will be 4.
Step-by-step explanation:
6+6 =12 for the lenghth
4+4=8= for the with
The function that represents the amount of caffeine in milligrams remaining
Answers
Answer:
Step-by-step explanation:
The function that represents the amount of caffeine, in milligrams, remaining in a body after drinking two mountain dew sodas is given by f(t) = 110(0.8855)^t, where t is time in hours.
Answer:
If you are referring to a logarithmic function with a continuous rate of decrease(as implied by remaining), then here is your answer:
A(t) = c×e^(dt)
where c is the starting amount of caffeine in miligrams, e is euler's number (base of a natural logarithm), and d is continuous rate of logarithmic change(as a percentage decay(negative)) per t(time) in standard unit of time(i.e hours)
I.e(for instance): if you are given a cup of coffee with an initial 190 mg of caffeine, leaving the body at a rate of 36% every hour.
This relationship solving for the remaining miligrams can be given by:
A(t) = 190 mg × e ^ (-.36t)
Where t is the amount of hours.
Which of these is a biomorphic shape? Choose the answer.
O a capital letter W
O a microphone
an outline of a pine tree
O a pyramid
Answers
Answer:
Option C: an outline of a pine tree
Step-by-step explanation:
Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.
A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.
Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".
Thus, it is a bimorphic shape.
Answer:
C. an outline of a pine tree
Step-by-step explanation:
I just took the test!
The length of a rectangle is (3x − 5) inches, and its width is 2x inches. Find the area of the rectangle.
Hint: Area of a rectangle = length × width.
Answers
Answer:
A = 6x² - 10x
General Formulas and Concepts:
Area of a Rectangle: Length × Width
To expand, use FOIL - First, Outside, Inside, Last
Step-by-step explanation:
Step 1: Define variables
l = 3x - 5
w = 2x
Step 2: Find area
Substitute: A = (3x - 5)(2x)Expand (FOIL): A = 6x² - 10xAnswer: A=6x^2-10x ✅
Step-by-step explanation:
Hii, do you need to find the area of the rectangle? Let me help you out! (:
Luckily, there's a formula to find this! (:
AreaTo find the area of a rectangle, multiply its length times its width. This is shown below.
[tex]\LARGE\boldsymbol{A=L W}[/tex]
Here, "A" denotes the area
"L" denotes the length
"W" denotes the width
NB : "L" and "W" are interchangeable
Next, it's just a matter of sticking in the known values...
[tex]\twoheadrightarrow\sf A=2x(3x-5)[/tex]
===> it's perfectly legal to stick in the values the other way around, because they are interchangeable
Alright, the next step is to multiply the values...
[tex]\twoheadrightarrow\sf A=(2x\cdot3x)-(2x\cdot(-5)[/tex]
Then we need to simplify...
[tex]\twoheadrightarrow\sf A=6x^2-10x[/tex]
Voila! There's the area of this rectangle! (:
Cheers! (:_______________Hope I helped! Best wishes.
⚜ Reach far. Aim high. Dream big. ⚜
_______________how to find the area figure of square inches
Answers
What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answers
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
Mike has at least 250 in his savings account.Which inequality represents this situation
Answers
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviation of 0.65 F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 3 standard deviation of the mean, or between 96.23 F and100.3 F?
Answers
Answer:
99.7%
Step-by-step explanation:
Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we have mean of 98.18 F and a standard deviation of 0.65 F
The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is
μ - 3σ
= 98.18 - 3(0.65)
= 98.18 - 1.95
= 96.23 F
μ + 3σ.
98.18 + 3(0.65)
= 98.18 + 1.95
= 100.13 F
Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%
jessie worked four more hours than Ben. They worked a total of 25 hours. How many hours did each boy workz?
Answers
Answer:
jessie: 14.5
ben: 10.5