Answer:
Step-by-step explanation:
The average rate of change of a function f between a and b (a< b) is :
R =[f(b)-f(a)] ÷ (a-b)
●●●●●●●●●●●●●●●●●●●●●●●●
Let R be the average rate of change of this function
f(6) = 2×6^2 - 7×6 = 72-42 = 30
f(2) = 2×2^2 - 7×2 = 8-14 = -6
R = [f(6) - f(2)]÷ (6-2)
R = [30-(-6)] ÷ 4
R = -36/4
R = -9
■■■■■■■■■■■■■■■■■■■■■■■■■
The average rate of change of this function is -9
Answer:
[tex]\frac{\Delta y}{\Delta x} =9[/tex]
Step-by-step explanation:
You can find the average rate of change of any function using the following formula:
[tex]Average\hspace{3} rate\hspace{3} of \hspace{3} change=\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Now, let:
[tex]x_1=2\\\\and\\\\x_2=6[/tex]
Let's evaluate the function for [tex]x_1[/tex] and [tex]x_2[/tex] :
[tex]f(x_1)=2(2)^{2} -7(2)=2*4-7*2=8-14=-6\\\\f(x_2)=2(6)^{2} -7(6)=2*36-7*6=72-42=30[/tex]
Therefore, the average rate of change of the function over the interval given is:
[tex]\frac{\Delta y}{\Delta x} =\frac{f(6)-f(2)}{6-2} =\frac{30-(-6)}{6-2} =9[/tex]
solve this question with calculation please:
Answer:
x=80
Step-by-step explanation:
the figure depicts a pentagon.
we can use linear pair method to find x
we should find interior angles
angle E= 180-90= 90
angle D=180-60= 120
angle C=180-x
angle A= 90 given
angle B= 180-40= 140
angle sum of a pentagon = 540
by formula (n-2)180. n is the number of sides
equation= 90+120+180-x+90+140= 540
620-x= 540
620-540=x
80=x
2. The price of a gallon of milk has been rising about 1.36% per year since 2000. a. What type of function would be best to model this scenario? Choose one of the types of functions studied in this course. Explain why you chose this answer. b. Write a formula for the function you chose to model this scenario. What does the independent variable in your function represent? c. If milk costs $4.70 now, what will it cost next year? Show how you found the answer. d. If milk costs $4.70 now, how long will it take for the price to top $5? Show how you found the answer.
Answer:
(a)Exponential
(b)[tex]P(t)=4.70(1.0136)^t[/tex]
(c)The price of milk next year will be: $4.76
(d)5 years
Step-by-step explanation:
The price of a gallon of milk has been rising about 1.36% per year since 2000.
(a)Since the price grows by a percentage (or constant factor) each year, an exponential function would be best to model the scenario.
(b)The exponential growth model is given as:
[tex]P(t)=P_0(1+r)^t$ where:\\P_0$=Initial Price\\r=Growth factor\\t=time (in years, for this case)[/tex]
The independent variable in the function is t. This represents the number of years since 2000.
(c)
[tex]I$nitial Price, P_0=\$4.70\\r=1.36\%=0.0136\\P(t)=4.70(1+0.0136)^t\\\\P(t)=4.70(1.0136)^t[/tex]
Therefore, the price of milk next year will be:
[tex]P(1)=4.70(1.0136)^1=\$4.76[/tex]
(d)We want to determine how long it will take for the price to top $5.
P(t)=$5
[tex]5=4.70(1.0136)^t\\$Divide both sides by 4.7$\\(1.0136)^t=\frac{5}{4.7} \\$Change to logarithm form\\t=Log_{1.0136}\frac{5}{4.7}\\t=4.58[/tex]
Therefore, in exactly 4.58 years, the milk price would be $5. Therefore, by the 5th year, the milk price would top $5.
PLEASE HELP ASAP THANKS A LOT
Answer:
The 8ft tall pine tree will not affect the box plot here is why........
Outliers are important because they are numbers that are "outside" of the Box Plot's upper and lower fence, though they don't affect or change any other numbers in the Box Plot they are still important.
If you want to find your fences you will first take your IQR and multiply it by 1.5. I call this your "magic number".
Lower fence: Take your Q1 and subtract it from your magic number, that number your get is your lower fence.
Upper fence: Take your Q3 and add it to your magic number, that number you get is your upper fence.
Find the roots of the quadratic equation 2x^2-x-4 =0
Answer:
I hope it will help you...
PLEASE HELP
Compare the functions show below:
Which function has the most x-intercepts?
A) f(x)
B) g(x)
C) h(x)
D) all three functions have the same number of x-intercepts.
Answer:
A) f(x)
Step-by-step explanation:
f(x) has 4 x-intercepts, becoz it "cross" the x axis 4 times.
g(x) would have an infinite number of intercepts coz it is a cos function, but it gave a limit to the domain which is 0 to 2[tex]\pi[/tex], so it only has 2 x-intercepts.
h(x) is the degree of x^3, so in theory, it has 3 x-intercepts.
The function that has the most x-intercept is given by: Option A: f(x)
What is x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.
The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 becuase at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
What is the maximum number of roots a polynomial equation can have?Suppose that we've got a polynomial function as y = p(x),
where p(x) is of degree n (the highest power its variable pertains in any of its composing terms).
Then, the maximum number of roots it can possess for p(x) = c (c is a constant), or p(x) - c = 0 is n
So, the number of roots of p(x) - c = 0 cannot exceed the degree of p(x).
From the graph, we see that:
f(x) intersects x-axis at 4 places, so it has 4 x-intercepts.
g(x) intersects the x-axis at 2 places as in the graph, and therefore, it has 2 x-intercepts.
h(x) is a polynomial of degree 3. The maximum number of intercepts it can have is the maximum number of roots h(x) = 0 can have which is 3(the degree of h(x) ). So it cannot be bigger than 3.
Thus, the function that has the most x-intercept is given by: Option A: f(x)
Learn more about x-intercept here:
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The area of one face of a cube is 4x².
Write a simplified expression for the total surface area of the cube.
Answer:
Step-by-step explanation
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the value of x in the image below.
Answer:
16
Step-by-step explanation:
64 = 4x
64/4 = 4x/4
16 = x
a bonus of 4200 is shared by 10 people who works for a company.40% of the bonus is shared equally between 3 managers the rest of the bonus is shared equally between 7 sales people.Peter, one of the sales people says," if the bonus is shared equally between 10 people i will get 25% more money. Janet a manager, says," no you wont get that much extra. show that Janet is correct by working out how much peter thinks he would get and how much he would actually get.
Step-by-step explanation:
if each the bonus is shared equally each will get 420
if 40% is shared by managers each manager will get 560
if 7 sales persons share 60% each will get 360
therefore Peter salesperson will get 360
but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct
0.02 × 0.3055 to 3 decimal places
Answer:
000.611
Step-by-step explanation:
0.02×0.3055
=0.00611
So in three decimal places
000.611
Eurostar is a high-speed railway service connecting
London with Paris and Brussels.
In February, 350,000 passengers travelled by Eurostar.
Each train has 15 carriages and each carriage has 32 seats.
How many trains would be needed
to seat 350,000 passengers?
If all the empty seats are on
the last train, find:
the number of empty carriages
you could make;
the number of empty seats across
all the other carriages.
Answer:
730 trains would be needed to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required
Step-by-step explanation:
Number of carriages in 1 train = 15
Number of seats in 1 carriage = 32
Number of seats in 15 carriages =[tex]32 \times 15 =480[/tex]
So, Number of seats in 1 train = 480
Number of trains needed to seat 350,000 passengers=[tex]\frac{350000}{480}=730[/tex]
Number of carriage in 1 train = 15
Number of carriage in 730 trains = [tex]15 \times 730=10950[/tex]
Number of seats in 1 carriage = 32
Number of seats in 10950 carriage =[tex]32 \times 10950=350400[/tex]
Hence 730 trains would be needed to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required
Use the integer tiles to find the quotient: 36 ÷ 6 = 6
Answer:
x=6
Step-by-step explanation:
Suppose x is 36÷6
x=36÷6
x=6
Answer:
36 / 6 = 6
36 = 6 * 6
36 = 36
Hope this somewhat helps!
Tim works for a company his normal rate of pay is 10 per hour on Friday Tim worked 4 hours overtime his overtime pay is 1 1/2 times his normal pay. Work out how much money Tim was paid for his over time on Friday
Answer:
60 .
Step-by-step explanation:
Normal pay for 4 hours = 10 * 4 = 40.
Overtime for 4 hours = 40 * 1 1/2
= 60.
Tim was paid 15 for his overtime.
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:
Normal pay of Tim= 10
Overtime hours= 4
and, overtime pay = 1 1/2 of 10
So, the overtime pay
= 3/2 of 10
= 3/2 x 10
= 15
Hence, Tim was paid 15 for his overtime.
Learn more about unitary method here:
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Is (x + 7) a factor of f(x) = x^3 − 3x^2 + 2x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
No there is a remainder of -512
Step-by-step explanation:
Divide (x+7) into (x^3 - 3x^2 + 2x - 8)
x^2-10x+72 R -512/(x+7)
According to the Factor theorem, (x+7) is not a factor of f(x) = x^3 − 3x^2 + 2x − 8.
What is remainder theorem?The theorem is as follows: A polynomial f(x) has a factor (x−p) if and only if f(p)=0.
Consider, f(x) = x^3 − 3x^2 + 2x − 8
Here, the expression we have is (x + 7), so we have to find f(-7) in order to check if (x+7) is a factor of f(x) or not
Here, p = −7
Now, lets check
f(−7)=(−343)−3(49)−14−8
f(−7)=−343−147−14−8
f(−7)=−512, which is not equal to 0 .
So, According to the Factor theorem,
(x+7) is not a factor of f(x) = x^3 − 3x^2 + 2x − 8.
Learn more about remainder theorem;
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PLEASE HELP
Choose the correct conic section to fit the equation.
X^2/16-y^2/4=1
1.Circle
2.Ellipse
3. Parabola
4. Hyperbola
Answer:
2.Ellipse
Step-by-step explanation:
The given equation represents an ellipse.
Standard form of ellipse is given as:
[tex] \frac{x^2}{a^2} +\frac{y^2}{b^2} = 1\\\\
\implies \frac{x^2}{16} - \frac{y^2}{4} = 1\\[/tex]
a drawer contains 30 pens of various colors: 4 are black 10 are blue, 3 are red, 6 are green , 6 are blue and red and 1 white A pen having blue or red is taken out of the drawer
Answer:
Probability of blue or red = 3/10
Step-by-step explanation:
4 are black 10 are blue, 3 are red, 6 are green , 6 are blue and red and 1 .
Total = 30
Probability of having a blue = 6/30
Probability of having a blue= 1/5
Probability of a red = 3/30
Probability of a red= 1/10
Probability of a blue or a red=
Probability of blue + probability of red
= 6/30 + 3/30
= 9/30
= 3/10
Plzzz help if u do both I’ll give Brainlynest
Answer:
Step-by-step explanation:
Q1; 10 units
The dotted lines separate the figure into 3 shapes - 1 square, 2 triangles.
The area of a square is s^2, where s is the side length.
The side length of the square is 2. 2^2 =4
The area of the square is 4 units.
The area of a triangle is bh/2, where b is the base and h is the height.
The base of the triangle on the left is 2 and the height is also 2. 2(2)/2 =2
The area of the left triangle is 2 units.
The triangle on the right has a base of 2 and a height of 4. 4(2) =8 /2 = 4
The area of the right triangle is 4 units.
The area of the composite figure is the area of the 2 triangles and the square added together; 4+2+4 =10
The area of the figure is 10 units.
Q2: The area of the shaded area is 44.2654825 [tex]cm^2[/tex].
The area of a circle is π[tex]r^2[/tex]. The radius of this circle is 4cm.
Therefore, the area of the circle is 16π[tex]cm^2[/tex].
The formula for area of a rectangle is length times width. The length of this rectangle is 3 and the width is 2.
Therefore, the area of the rectangle is 6 cm^2
We're looking for the area of the shaded region (area of circle- rectangle), so we subtract the area of the rectangle from the area of the circle.
16π simplifies to 50.2654825 cm^2.
50.2654825-6 = 44.2654825 cm^2
The area of the shaded area is 44.2654825 [tex]cm^2[/tex].
Having more relevant instruments... a. is a problem because instead of being just identified, the regression now becomes overidentified. b. will typically result in a more efficient TSLS estimator c. will typically result in larger standard errors for the TSLS estimator. d. May result in the TSLS being inconsistent in large samples
Answer:
d. May result in the TSLS being inconsistent in large samples
Step-by-step explanation:
Two-stage least squares (TSLS), regression analysis is a statistical technique that is used for two distinct stages of variables regression, so, when there are more relevant instruments than required, is like having a larger sample size in that the more information is available for use in the Instrumental Variables regression (IV).
Complete the solution of the equation. Find th
value of y when x equals -4.
- 8x + y = 37
Enter the correct answer.
Answer:
64
Step-by-step explanation:
Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (2,3) A. (-2, -3) B. (3, -2) C. (2, -3) D. (-3, 2)
Answer:
D
Step-by-step explanation:
Given
[tex]R_{y-axis}[/tex] ￮ [tex]R_{y=x}[/tex] : (2, 3 )
Then the order of reflections is from right to left, that is
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , thus
(2, 3 ) → (3, 2 )
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , thus
(3, 2 ) → (- 3, 2 ) → D
Suppose the linear regression line y = 3.27x + 1.52 predicts the weight of a large dog, in pounds, x weeks after it is born. About how much would the dog weigh after 6 weeks?
Answer:
21.14 lbs.
Step-by-step explanation:
So you plug in x=6.
y=3.27(6)+1.52=21.14
Which of the following is the solution to the inequality below?
1
- 5x
A. X>
3
35
3
B. X<-.
35
C. X
21
O D. x
21
SUBMIT
Answer:
The correct answer is A. x > -3/35
Step-by-step explanation:
-3/2(x - 1/3) > 1/5 - 5x
-3/2x + 1/2 > 1/5 - 5x
-15x + 5 > 2 - 50x
-15x + 50x + 5 > 2
-15x + 50x > 2 - 5
35x > 2 - 5
35x > -3
x > -3/35
Hope this helped! :)
Answer: A. x > -3/35
Step-by-step explanation:
A conical-shaped umbrella has a radius of 0.4 m and a height of 0.45 m. Calculate the amount of fabric needed to manufacture this umbrella. (Hint: an umbrella will have no base)
Answer:
The correct answer will be "0.756596 m²".
Step-by-step explanation:
The given values are:
The radius of an umbrella,
r = 0.4 m
The height of an umbrella,
h = 0.45 m
As we know,
The lateral surface of an umbrella will be:
⇒ [tex]\pi r\sqrt{r^2+h^2}[/tex]
On substituting the values, we get
⇒ [tex]\pi \times 0.4\sqrt{(0.4)^2=(0.45)^2}[/tex]
⇒ [tex]0.756596 \ m^2[/tex]
So that the amount of fabric needed will be "0.756596 m²".
Solve -25 -( -5) +(- 20)
Answer:
-40
Step-by-step explanation:
-25 -(-5) + (-20)
-25 + 5 - 20
-20 - 20
= - 40
Note that:
+ ( + ) = +
+ ( - ) = -
- ( + ) = -
- ( - ) = +
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~
-25 -( -5) +(- 20) =
-40
Step-by-step explanation: Simplify the expression.
Hope this helped you. Brainliest would be nice!
☆_____________❤︎______________☆
calculate the height of an equilateral triangle with side is 8 cm long
Step-by-step explanation:
use pythagoras theorem for finding the height
hypotenuse is 8cm
base is 4 cm
height?
a^2+b^2=c^2
64-16=a^2
a=7.07cm
Height of equilateral triangle is 7.07cm
A square with side length c has an area of 81 square centimeters. The following equation shows the area of the square. c^2 = 81. What is the side length of the square in centimeters?
Answer:
9 cm
Step-by-step explanation:
c^2=81
Take the square root of both sides.
The square root of c^2 is c.
The square root of 81 is 9.
c=9
Answer:
C = 9 centimeters
Step-by-step explanation:
First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 * 9 = 81. Thus the answer is 9 centimeters.
the outside of the silo shown below needs to be painted.the silo is 80 feet tall and has 20 foot diameter.of one gallon of paint covers 100 square feet how many gallons of paint will be needed you can ignore the doors and windows
Answer:
[tex]\approx[/tex] 57 gallons
Step-by-step explanation:
Given:
Silo needs to be painted.
Height of silo = 80 feet
Diameter of silo = 20 feet
One gallon of paint covers 100 sq ft
To find:
Gallons of Paint required to paint the outside of silo = ?
Solution:
We need to first calculate the lateral surface area(LSA) of this cylinder shaped silo.
[tex]LSA = 2\pi rh[/tex]
where r is the radius and
h is the height of cylinder.
[tex]r = \dfrac{Diameter}2\\\Rightarrow r = 10\ ft[/tex]
Putting the values in formula:
[tex]LSA = 2\times 3.14\times 10\times 80\\\Rightarrow LSA = 5024\ sq \ ft[/tex]
Total surface area of cylinder = LSA + 2 [tex]\times[/tex] Area of base
Total surface area of cylinder = LSA + 2 [tex]\times[/tex] [tex]\pi r^{2}[/tex]
TSA = [tex]5024 +2 \times 3.14 \times 10^2 = 5024 +628=5652\ sq \ ft[/tex]
100 sq ft requires number of gallons = 1
5652 sq ft requires number of gallons:
[tex]\dfrac{1}{100} \times 5652 \approx 57\ gallons[/tex]
PLS HELP ME WITH THIS QUESTION IVE BEEN DYING TRYING TO FIGURE THIS OUT
Answer:
y = -x - 1
Step-by-step explanation:
hello,
this is a line, right?
So the equation should be something like
y = ax+b and we need to find a and b
we can see that the points (-1,0) and (0,-1) are in the line so we can write
0 = a*(-1) + b <=> b - a = 0 <=> a = b
-1 = a*0 + b <=> b = -1
so the equation is
y = -x - 1
hope this helps
Answer:
y = - x - 1
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (0, - 1)
m = [tex]\frac{-1-1}{0+2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - x - 1 ← equation of line
At Kathmandu temperature was – 5°C on Monday and then it dropped by 2∘C on Tuesday. What was the temperature of Kathmandu on Tuesday?
Answer:
Monday= -5°c
on Tuesday dropped 2 °c
question
what was temperature on Tuesday
answer
=-5 - 2= -7°c on tuesday
hope it helps you
#passionforlearning
plz help bored and need an answer.
Answer:
the answer to this question would be 9 which is B
pleeeeeeeeeeeeeeeeeeease i need this answer
Answer:
12^2(Pi)+24*(Pi)*35
Step-by-step explanation:
12^2(Pi)+24*(Pi)*35