Answers
Problem 2
Answer: Average rate of change = 4==========================================================
Explanation:
When we have an interval [a,b], the average rate of change over this interval is given by the formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
You probably can notice that we have something that looks eerily similar to the slope formula. That's because average rates of change are basically the same as the slope of the straight line through the endpoints of the interval. The f(b)-f(a) is the change in y of f(x) outputs. The b-a down below is the change of x values when going from x = a to x = b.
-------------------
Let's evaluate the function at x = 1
f(x) = x^2+1
f(1) = 1^2+1
f(1) = 2
Repeat for x = 3
f(x) = x^2+1
f(3) = 3^2+1
f(3) = 10
--------------------
We have enough info to evaluate the original formula I mentioned earlier
[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(3)-f(1)}{3-1}\\\\m = \frac{10-2}{3-1}\\\\m = \frac{8}{2}\\\\m = 4\\\\[/tex]
The average rate of change on this interval is 4
This is the same as saying the slope of the line through (1,2) and (3,10) is m = 4
See the graph below.
Related Questions
please answer the question first
Answers
Answer:
Yes, 2.4
Step-by-step explanation:
Y is directly dependant on x, and the constant we multiply x by to get y is 2.4.
Answer:
Yes, 2,4
Step-by-step explanation:
This explains direct proportion because it shows that y equals the 2.4x which is the direct proportion
Hopes this helps
A plane left Kennedy airport on Tuesday morning for an 630mile 5 hour trip for the first part of the trip the average speed was 120 mph for the remainder of the trip the average speed was 130 mph how long did the plane fly at each speed
Answers
Answer:
The plane travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \rm mph[/tex] and [tex]\text{$3$ hours}[/tex] at an average speed of [tex]130\; \rm mph[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the number of hours that the plane travelled at an average speed of [tex]120\; \rm mph[/tex].
Given that the trip is [tex]5\; \text{hours}[/tex] long in total, the plane would have travelled at an average speed of [tex]130\; \rm mph[/tex] for [tex](5 - x)\; \text{hours}[/tex].
The plane would have travelled [tex]120\, x[/tex] miles after [tex]x\; \text{hours}[/tex] at an average speed of [tex]120\; \rm mph[/tex]. Likewise, the plane would have travelled [tex]130\, (5 - x)\; \text{miles}[/tex] after [tex](5 - x)\; \text{hours}[/tex] at an average of [tex]130\; \text{mph}[/tex].
The plane has travelled [tex]630\; \text{miles}[/tex] in total. In other words:
[tex]120\, x + 130\, (5 - x) = 630[/tex].
Solve this equation for [tex]x[/tex]: [tex]x = 2[/tex].
In other words, the plane has travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \text{mph}[/tex]. It would have travelled for [tex](5 - x)\; \text{hours} = (5 - 2)\; \text{hours} = 3 \; \text{hours}[/tex] for the other part of the trip (at an average speed of [tex]130\; \text{mph}[/tex].)
18- 3 x 2/5 - 12
Could someone help me with this?
Answers
Answer:
I hope it helps u.......
Convex angles help me
Answers
Answer:
C, D, F
Step-by-step explanation:
Shape A is not a polygon; it has a line that doesn't connect anywhere. Even if it is a polygon, it would be concave. Shape B is a concave polygon, shape E is also a concave polygon, shape G and H are also concave polygons. Only shapes C, D, and F are convex polygons. Concave polygons are shapes that cave in, and convex polygons are caves that don't cave in.
Pls help I’m need to get my grade up
Answers
Answer:
38
Step-by-step explanation:
So, we know the formula is:
D=rt or D=r*t
We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.
Here are the two sets we can look at:
t=2, d=76
t=3, d=114
Lets plug these in and solve:
76=r*2
Divide both sides by 2 to get r alone:
38=r
Now lets check if this is true by pluggin in 38 for r in the second set, and seeing if it works:
D=r*t
114=38*3
=
114=114
So 38 is our answer.
Hope this helps!
what will the time be after 1 hour 5 minutes from 8:15 am
Answers
Answer:
9:20 am
Step-by-step explanation:
So, lets go over two things.
Minutes and hours.
Minutes changes the second number.
You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.
Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.
In this case. we are moving the minutes place up by 5:
15+5=20
So the minutes place is 20, and does not change the hours place since it is below 60.
Next we have a increase in hours by 2:
8+1=9
So the hours place is 9, and does not reset or change the pm/am since its below 12.
Answer:
9:20am
Hope thias helps!
Answer:
9:20 am
Step-by-step explanation:
Add 1 hour
8:15 to 9:15
Add 5 minutes
9:15 to 9:20
Please help me I don’t understand …
Answers
Answer:
X=90°
Y=58°
Z=32°
Step-by-step explanation:
X=180°-90°=90°
Y=180°-90°-32°=58°
Z=180°-58°-90°=32°
Answer:
x = 90°, y = 58°, z = 32°
Step-by-step explanation:
The angles in a square = 90° , then
x = 90° ( adjacent angle )
The sum of the 3 angles in a triangle = 180° , then
x + y + 32° = 180° , that is
90° + y + 32° = 180°
y + 122° = 180° ( subtract 122° from both sides )
y = 58°
y + 90° + z = 180° ( straight angle )
58° + 90° + z = 180°
148° + z = 180° ( subtract 148° from both sides )
z = 32°
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
Answers
Answer:
Step-by-step explanation:
We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is
[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to
[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.
(I+ tan square theta)(1-sin square theta)
Answers
Answer:
1
Step-by-step explanation:
Formulas used:
[tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]
[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]
Answer:
[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]
The rectangle was rotated 360° around its center, point
C. Vertex D traces the path of a circle and lands back
Which best explains why the rotation represents an
isometric transformation?
upon itself.
y
O The angle at point D remained a right angle.
O The rectangle did not change shape or size.
O Point C remained the center of the rectangle.
5
D
4
Point C did not remain the center of the rectangle.
3
2+
1
с
+
1
43 -2 -11
2
3
4.
-2+
-3+
Answers
Answer:
O The rectangle did not change shape or size.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Isometric transformation is a transformation that preserves the shape and size of the figure. Types of isometric transformations are reflection, translation and rotation.
The rectangle represents an isometric transformation because the rectangle did not change shape or size.
A study examines the relationship between educational preparation and scores on a cultural competency exam. Subjects included are nurses with an associate's degree, nurses with a baccalaureate degree, nurses with a master's degree, and nurses with a doctoral degree. In this example, cultural competency is measured at what level?
a. Dependent variable
b. Independent variable
c. Outcome
d. Significant variable
Answers
Answer:
b. Independent variable
Step-by-step explanation:
Understanding the definition of variables is necessary to grasp the notion of independent and dependent variables. The attributes or sorts of features of specific occurrences or things are specified as variables.
Independent variables are variables that are modified or altered by researchers and the consequences of these modifications are evaluated and compared.
The term dependent variable relates to a sort of variable that assesses how the independent variable(s) impact the test results.
From the given information:
Education level is the predictor since we understand that nurses' education levels are closely correlated with their cultural competence scores. By applying the concept of the logistic regression model and using education level as an independent variable(predictor), we can simply predict their cultural competency. Thus, cultural competency is measured by using the independent variable.
fill in the blanks the 2 digit largest whole number is______
Answers
A desk is on sale for $368 , which is 36% less than the regular price.
What is the regular price? PLEASE SHOW EXACTLY HOW TO DO THIS
Answers
The regular price of the desk found using the discount and the selling price is $575.
What is meant by the discount rate of an item?
Discount pricing is a form of promotional pricing strategy where the original cost of a good or service is decreased in an effort to draw more customers, move inventory, and boost sales. Consumers adore feeling as though they are getting a fantastic bargain, which is why they are lured to reduced costs. The selling price is the price at which the good or commodity has actually been sold, whereas the marked price is the cost set by the seller in accordance with market norms. The buyer claims to have received a discount when the selling price is less than the marked price.
Given,
The selling price of the desk = $368
The percentage of discount = 36%
Let the regular price be x.
then we can write the following equation,
x - 36% of x = 368
x - 0.36x = 368
0.64x = 368
x = $575
Therefore the regular price of the desk found using the discount and the selling price is $575.
To learn more about the discount rate, follow the link.
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HELP PLEASE! What is BD??
Answers
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
ANSWER ASAP PLS!!!!!
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answers
Answer:
see below
Step-by-step explanation:
f(n) = 10(1.02)^n
Part A
Let f(n) = 11.04
11.04 = 10 * 1.02 ^n
Divide each side by 10
11.04/10 = 1.02^n
1.104 = 1.02^n
Taking the log of each side
log 1.104 = log 1.02^n
We know log a^b = b log a
log 1.104 = n log 1.02
log 1.104 / log 1.02 = n
4.99630=n
Rounding n to 5
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
To find the average rate of change
f(5) - f(1)
-----------
5-1
f(5) = 11.04
f(1) = 10 *1.02 =10.2
11.04 - 10.2
-----------
5-1
.84
-----
4
.21 cm per day
The average rate of growth over the 4 days is .21 cm per day
Answer:
Part A: A reasonable domain to plot the growth of the function would be: 0 < n < 5.
Part B: The y-intercept of the graph of the function f(n) represents the height of the plant in 0 days when it first began.
Part C: The average rate of change of the function from n = 1 to n = 5 is 0.84 or 0.21cm per day. It represents the amount of growth for the plant over 4 days.
, Hope this helps :)
Have a great day!!
you spin each spinner and find the sum how many different sums are possible
Answers
Answer:
let's use a sample set.
8+8, 8+4, 8+5, 8+6, 8+7
4+8, 4+4, 4+5, 4+6, 4+7
5+8, 5+4, 5+5, 5+6, 5+7
6+8, 6+4, 6+5, 6+6, 6+7
7+8, 7+4, 7+5, 7+6, 7+7
There is 25 sums.
b. If you take one spin, what is your expected value?
Answers
Answer:
3/7
Step-by-step explanation:
Expected Value:
3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7
Expected value when we take one spin = 3/7
What is the expected value?It is the sum of values multiplied by their respective probabilities.
How do we calculate the expected value after one spin?We have 2 red, 2 purple, 2 yellow, and 1 blue sector.
Total number of Sectors = 7
∴Probability of landing on red sector = 2/7
∴Probability of landing on purple sector = 2/7
∴Probability of landing on yellow sector = 2/7
∴Probability of landing on blue sector = 1/7
Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.
X 3 1 0 -1
P(X) 1/7 2/7 2/7 2/7
Expected Value = ∑X.P(X)
=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)
= 3/7
Learn more about Expected Values on
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Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time. day change Monday +2000 Tuesday -125 Wednesday -127 Thursday +1719 Friday -356 Saturday -782 Sunday 0 2. How many paper cups are left at the end of the week?
Do only number 2
Answers
Answer:
2329
Step-by-step explanation:
2000 - 125 - 127 + 1719 - 356 - 782 = 2329
The distance between two points is 10 units, if the coordinates of one of the endpoints are (4, -7), find x if the coordinates of the other endpoint are (x, 1).
Answers
Answer:
10
Step-by-step explanation:
let the distance = d
d² = (x2-x1)² + (y2-y1)²
=>
10²= (x-4)²+(1+7)²
100 = (x-4)²+64
(x-4)²=100-64
= 36
x-4 = √36
x-4=6
x= 6+4
x= 10
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answers
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
What’s the volume of the rectangular prism in cubic meters
Answers
Answer:
Volume of the prism=60m3
Step-by-step explanation:
Volume of any prism=height*width*length
Volume of the prism=3m*5m*4m=60m3
Volume of the prism=60m3
In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d.
The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.
Answers
Given:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.
I hope this helps!
Answer:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
a carton of orange juice is 9 centimeters wide. 13 centimeters long and 24 centimeter is tall. if i drink one third of the fruit juice what is the volume left in the carton?
Answers
Answer: 1872cm³
Step-by-step explanation:
First and foremost, we've to calculate the volume of the carton which will be:
= Length × Width × Height
= 13cm × 9cm × 24cm
= 2808cm³
The volume that'll be left after ⅓ of the volume is drank will be:
= 2808 - (⅓ × 2808)
= 2808cm³ - 936cm³
= 1872cm³
Can anybody help me with this problem regarding Line Integrals (Calc 3)?
Compute ∫F*dr, given the counterclockwise unit circle C : cos((pi)t), sin((pi)t), t∈[0,2] and the vector field F(x,y) = (y²,-x²)
Answers
The line integral is
[tex]\displaystyle \oint_C\mathbf F(x,y)\cdot\mathrm d\mathbf r = \int_0^2 \mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt \\\displaystyle= \int_0^2 (\sin^2(\pi t),-\cos^2(\pi t))\cdot(-\pi\sin(\pi t),\pi\cos(\pi t))\,\mathrm dt \\\displaystyle=-\pi\int_0^2(\sin^3(\pi t)+\cos^3(\pi t))\,\mathrm dt = \boxed{0}[/tex]
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
Answers
9514 1404 393
Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
[tex]9^x-1=2[/tex]
You can use logarithms, or your knowledge of powers of 3 to solve this.
[tex]9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}[/tex]
Using logarithms, the solution looks like ...
[tex]x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}[/tex]
An aerodynamic 1,000 kg car takes about 270 newtons of force to maintain a speed of 25 m/s. how much horsepower is required from the engine to maintain this speed?
Answers
Answer:
9.05 horse power
Step-by-step explanation:
Given:
Force = 270 Newton
Speed = 25 m/s
Power = Force * velocity
Power = 270 Newton * 25 m/s
Power = 6750 watt
Recall:
1 horse power = 746 watts
Hence, required horsepower is :
6750 watt / 746 watt
9.048 hp
9.05 horse power
In the sale, Mo buys a jacket for $63.
The original price was reduced by 25%.
Calculate the original price of the jacket.
Answers
Answer:
$84
Step-by-step explanation:
63÷3=21
63+21=84
Hope this helps! :)
The two way table shows information about preferred drinks of some people how many males drank only coffee
Answers
Answer:
73% The two-way table shows information about the preferred drinks of some people. b a How many males drank only coffee? b What is the probability that any person is male and only drinks coffee? 73% The two-way table shows information about the preferred drinks of some people
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Please help me with #26-28
Answers
Answers:
26) probability = 1/427) probability = 0.058828) probability = 0.157=================================================
Work Shown:
26)
1/2 = probability of an odd number, since half of the numbers are odd
1/2 = probability of tails
(1/2)*(1/2) = 1/4 is the probability of both events happening at the same time
----------------------------
27)
13/52 = probability of pulling out one club
12/51 = probability of pulling out a second club, assuming the first one is not put back
(13/52)*(12/51) = 156/2652 = 1/17 = 0.0588 is the probability of pulling two clubs in a row (without replacement).
----------------------------
28)
11/27 = probability first person has blonde hair
10/26 = probability second person has blonde hair (cannot reselect the first person again)
(11/27)*(10/26) = 110/702 = 55/351 = 0.157 is the probability of selecting two people with blonde hair
the volume of a cylinder is 44cm3. find the volume of another cylinder of the same height and double the base radius
Answers
Answer:
[tex]Volume \ of \ other\ cylinder = 176 \ cm^3[/tex]
Step-by-step explanation:
Let the volume of cylinder Vₐ = 44cm³
Let radius of cylinder " a " be = rₐ
Let height of cylinder " b" be = hₐ
[tex]Volume_a = \pi r_a^2 h_a\\\\44 = \pi r_a^2 h_a[/tex]
Given cylinder " b ", Radius is twice cylinder " a " , that is [tex]r_b = 2 r_a[/tex]
Also Height of cylinder " b " is same as cylinder " a " , that is [tex]h_b = h_a[/tex]
[tex]Volume_b = \pi r_b^2 h_b[/tex]
[tex]= \pi (2r_a)^2 h_a\\\\=4 \times \pi r_a^2 h_a\\\\= 4 \times 44\\\\= 176 \ cm^3[/tex]