Answer:
The average rate of change is m = 3.4 models of paper shredders per year
Step-by-step explanation:
The rate of change m of a function is:
[tex]m = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
In this problem the function receives a variable x = year and returns a variable f(x) = models of paper shredders
We know that for [tex]x = 1998[/tex], [tex]f(x) = 2[/tex]
We also know that for [tex]x = 2008[/tex], [tex]f(x) = 36[/tex].
Then we can calculate the average rate of change using these values.
[tex]m = \frac{f(2008)-f(1998)}{2008-1998}[/tex]
[tex]m = \frac{36-2}{2008-1998}[/tex]
[tex]m = 3.4[/tex]
The average rate of change in the number of paper shredder models produced by the company from 1998 to 2008 is 3.4 models per year.
Explanation:To calculate the average rate of change, we can use the formula (Change in Y) / (Change in X). In this case, 'Y' is the number of paper shredder models and 'X' is the time, in years. In 2008 the company manufactured 36 models which is an increase from the 2 models they made in 1998.
The change in 'Y' (ΔY) would therefore be (36 - 2) = 34. The change in 'X' (ΔX) would be (2008 - 1998) = 10 years. Therefore, the average rate of change would be ΔY / ΔX = 34 / 10 = 3.4.
This suggests that, on average, the company has been producing an additional 3.4 models of paper shredders each year over this 10 year period in response to rising concerns about identity theft.
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according to the graph of F(x), which of the statements below are true? check all that apply
Answer:
B, E and F
Step-by-step explanation:
This graph is a log which has an asymptote. This means the function does not cross it and does not have in its domain certain numbers. The asymptote is at -2. This means the domain is greater than -2.
The range is the y-values. With no restrictions here, the function includes all numbers.
This means B, E, and F are true.
avery prepares 2 equal size oranges for the bats at the zoo. one dish has 3/8 of an orange. Another dish has 2/8 of an orange. which dish has more orange? show your work.
Answer:
3/8
Step-by-step explanation:
it is greater than 2/8
Simplify the expression square root of 6 times the square root of 33 plus 7
Answer:
3√(22) + 7
Step-by-step explanation:
The way this is worded can be interpreted two different ways so just to cover the bases, I'll do both. I'm confident they are asking for way 1 though because it wants you to simplify the expression, not evaluate. Way 2 gives you a solution rather than an exact equation.
Number 1
√(6) x √(33) + 7
= √(6 x 33) + 7
= √(198) + 7
= √(9 x 22) + 7
= 3√(22) + 7
Number 2
√(6) x √(33 + 7)
= √(6) x √(40)
= √(6) x (4√(10))
= 4√(60)
= 8√(15)
The simplified expression for [tex]\sqrt{6} \times \sqrt{33} + 7[/tex] is [tex]3\sqrt{22} + 7[/tex]
To simplify square root of 6 times the square root of 33 plus 7 we need to first write it mathematically. We get:
[tex]\sqrt6 \times \sqrt{33}+7[/tex]
Using BODMAS, we first multiply the roots. This will give us:
[tex]\sqrt{6} \times \sqrt{33} + 7 = \sqrt{6 \times 33} +7[/tex]
Now we need to expand the digits in square by expressing them as a product of their prime factors so that common pairs can be taken out of the root. This can be done as follows:
[tex]\sqrt{6 \times 33} +7 = \sqrt{(3 \times 2)\times (3\times11)} +7[/tex]
We can see that there are two pairs of 3. Thus we extract 3 times 3 as it is a perfect square for 9 and we get:
[tex]3\sqrt{( 2\times 11)} +7 = 3\sqrt{2}+7[/tex]
Thus, the simplified expression for [tex]\sqrt{6} \times \sqrt{33} + 7[/tex] is [tex]3\sqrt{22} + 7[/tex]
A point located at (3, -2) is translated right 3 units and down 4 units. What are the coordinates of the image? (0, -2) (6, -6) (6, 2) (0, -6)
Answer:
(6,-6)
Step-by-step explanation:
Because if you move to the right 3 units you add 3 to the x-axis number or in this case 3, so 3+3=6, and if you move down 4 units its the same as subtracting 4 from the y-axis number or in this case -2 so, -2-4=-6. Which gives you (6,-6).
Answer:
(6, -6)
Step-by-step explanation:
What is the volume of this right rectangular prism? Enter your answer in the box. ft³ 3.5 is the H, 2 is the L and 7 is the W
Answer: 49 feet to the third power
Step-by-step explanation:
1. 3.5 x 2= 7
2. 7 x 7= 49
Answer: [tex]49\ ft^3[/tex]
Step-by-step explanation:
The volume of rectangular prism is given by :-
[tex]\text{Volume}=l*w*h[/tex], hwre l is the length , w is width and h is height of prism.
The given dimensions of rectangular prism :
Length : 2 ft
Width : 7 ft.
Height : 3.5 ft.
Now, the volume of rectangular prism is given by :-
[tex]\text{Volume}=7\times2\times3.5\\\\\Rightarrow\text{Volume}=49\ ft^3[/tex]
Hence, the volume of this right rectangular prism = [tex]49\ ft^3[/tex]
Use the net below to determine the surface area of the cylinder.
The correct answer should be :
Option 3 : [tex]753.6cm^{2}[/tex]
Hope this helps,
Davinia.
Explicit formula for the sequence -3,-14,-25,-36
ANSWER
[tex]a_{n}=a_{n-1} - 11 \: \: ,a_1 = - 3[/tex]
EXPLANATION
The given sequence is
[tex]-3,-14,-25,-36,...[/tex]
The first term of the sequence is
[tex]a_1=-3[/tex]
The common difference is
[tex]d = - 14 - - 3[/tex]
[tex]d = - 11[/tex]
The recursive formula is
[tex]a_{n}=a_{n-1} - 11 \: \: ,a_1 = - 3[/tex]
Answer:
aₙ = aₙ₋₁ -11
Step-by-step explanation:
We have given the sequence:
-3,-14,-25,-36
We have to find the explicit formula.
The first term in this sequence is:
a₁ = -3
The common difference is:
a₂-a₁= -14-(-3) = -11
a₃-a₂ = -25-(-14) = -11
a₄-a₃ = -36-(-25)= -11
Common difference d = -11
The general formula is :
aₙ = aₙ₋₁ +d
Here d = -11 so,
aₙ = aₙ₋₁ -11 is the explicit formula.
Choose the graph which represents the solution to the inequality:
-x - 3 < 0
Answer:the answer is B
Step-by-step explanation:
The graph shows how the inequality was resolved: Option B is -X-3 >
What is inequality of a graph?The collection of dots that represents each inequality solution can be found on the graph of a two-variable inequality. The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half.Inequality is the relationship between two expressions or values that are not equal to one another.Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are deemed to be equal. The symbols >,,, or indicate that the two expressions in an inequality are not necessarily equal.To learn more about inequality refer to:
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full-time job usually means you will work how many hours per week? A. 20 B. 35 C. 40 D. 55 Please select the best answer from the choices provided A B C D
Answer:
C. 40 or B. 35
Step-by-step explanation:
Full time jobs are typically jobs that vary from 35-40 hours a week.
Hope this helps :)
Answer:
C) 40 hours
Step-by-step explanation:
Usually, a full-time job employee works 8 hours per day. There are 7 days in a week where most of employees work 5 days a week, remaining 2 days week off.
Therefore, the number of hours per week = 5 days * 8 hours per day
= 40 hours
Hence, the answer is C) 40
80% of the days in April were sunny, how many days were sunny?
Answer:
24 days
Step-by-step explanation:
April = 30 days
100% = 1.0
80% = 0.8
If 1 x 30 = 30
then 0.8 x 30 = 24
Answer:
24
Step-by-step explanation:
0.8 x 30 = 24
80% = 0.8
April = 30 days
HOPE THIS HELPED!!!!! XD
Can I have brain? please
What is the sum of the polynomials?
(–x2 + 9) + (–3x2 – 11x + 4)
–4x2 – 2x + 4
–4x2 – 11x + 13
2x2 + 20x + 4
2x2 + 11x + 5
[tex] - {x}^{2} + 9 - 3 {x}^{2} - 11x + 4 \\ = - 4 {x}^{2} - 11x + 13[/tex]
2nd answer
Answer:
Option B. -4x² - 11x + 13
Step-by-step explanation:
Given polynomials are ( -x² + 9 ) and ( -3x² - 11x + 4 )
We have to add them.
( -x² + 9 ) + -3x² - 11x + 4 )
-x² + 9 - 3x² - 11x + 4
Now we will collect similar terms
( -x² - 3x² ) - 11x + ( 9 + 4 )
-4x² - 11x + 13
Therefore, option B is the answer.
The average snow base at Heavenly Ski Resort is 2 feet in the month of December. In the month of January, the average base is 3 feet. If the snow base increases at about the same rate through the month of March, which is the best estimate for the snow base in the month of March?
A. 2 ft
B. 3 ft.
C. 4 ft.
D. 5 ft.
I took a picture of 2 problems I need help with can someone help me please
1 is C not sure about 2
Find the height of the given pyramid.
2.3m
4.5m
6m
7m
Answer:
The height is 7 m.
Step-by-step explanation:
Volume = 1/3 * area of the base * height, so
28 = 1/3 * 3 * 4 * h
4h = 28
h = 7.
WILL MARK BRAINLIEST!! Complete the statements to find the measurements of ∠a and ∠b .
Answer:
angles b and a both equal 60 degrees
Step-by-step explanation:
a and b are both equal to 60 degrees. A flat angle is 180 and you have the one that’s 120 so that one is 60 and then the last side must be 60 as well because when you add them then subtract it from 180 you get 60
Plz help me i need it
Answer: [tex]\bold{d)\quad f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
Step-by-step explanation:
To find the inverse, swap the x's and y's and solve for y. Note: f(x) is y
[tex]y = ln(5x)\\\\\text{Swap the x's and y's:}\\x=ln(5y)\\\\\text{Apply e to both sides:}\\e^x=e^{ln(5y)}\\\\e^{ln}\ \text{cancels out:}\\e^x=5y\\\\\text{Divide both sides by 5:}\\\dfrac{e^x}{5}=y\\\\\large \boxed{f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
Which of the following are solution to the inequality below -4w - 2 < -38
Answer:
w > 9
Step-by-step explanation:
Solve the inequality by using inverse operations.
-4w - 2 < -38
-4w < -36
w > 9
Like solving equations, inequalities should be solved using inverse operations. However, unlike equations, when you divide or multiply by a negative the sign changes.
Ok I don't have time to do this i got to study for a history test so can some one simplify these real fast pls
5(2z-1)
(4-2k)8
(15-4a)5
6(n+1.2)
(n-8.2)5
And can u do these
6(n+4)=42. -6(x+8)=0. 3(-4+2r)=-24. 8(-7y-6)=-160
(2a+1.75)2=7.5 (2.3-6n) 1/5=3.14
Thx pals
1. 10z - 5
2. -16k + 32
3. -20a + 75
4. 6n + 7.2
5. 5n - 41
6. n = 3
7. x = -8
8. r = -2
9. y = 2
10. a = 1
11. n = -2.23333333 ( this is the only problem im unsure of answer )
please help the answer i put idk if its correct (brianlest if correct)
Answer:
9,5
Step-by-step explanation:
It's it reflection on the opposite side, so you get (9,5) as they were also given to you.
Helppppp please. .........
Answer: 12 feet
Step-by-step explanation: look at the bottom length of the rectangle, it is 10 feet, the missing length of the rectangle should be 10 ft as well. we already know that two of the sides are 3 so we can do 3+3+x=10, x=4. the base of the triangle is 4. We can now use the formula for area of the triangle, 1/2 base*height so 1/2 *6*4= 12 feet, Hope this helps!
The function f(x) is shown in this graph
Answer:
The correct statement is:
The slope of f(x) is same as the slope of g(x)Step-by-step explanation:
We see that the graph of the function f(x) is a line that passes through (0,2) and (1,-1)Hence, the equation of the function f(x) is calculated by a two-point formula as:
[tex]y-2=\dfrac{-1-2}{1-0}\times (x-0)\\\\y-2=\dfrac{-3}{1}\times x\\\\y-2=-3x\\\\y=-3x+2[/tex]
( On comparing the equation of f(x) with slope intercept form.
i.e. y=mx+c
where m is the slope and c is the y-intercept)
We get slope of f(x)= -3
and y-intercept= 2
The function g(x) is given by:[tex]g(x)=-3x-6[/tex]
Hence, slope of g(x) = -3
and y-intercept= -6
Hence, we get that the slope of f(x) and g(x) is same.
( i.e. -3)
find 3 different possibile pairs of values for a and b
a=1, b =18
a=2, b = 9
a = 3 , b = 6
Hello! Essentially you are trying to find a linear function. For example, a linear function is a function that increases or decreases in some type of relationship between each pair consistently. To answer your question, one example could look like this...
Lastbenchstudent basically nailed the linear equation but I could elaborate from his work and answer your question in a different way.
A = 3, B = 18
A = 2, B = 9
A = 1, B = 4.5
To explain my answer, I basically divided B every time A decreased. As A decreased by 1, B decreased by half the amount!
PLZ HELP ME IM STRUGGLING
$15 dollars per adult
$9 per child
We have 4 adults and 5 children.
Adults: 15 x 4 = $60
Children: 9 x 5 = $45
$60 + $45 = $105
Answer: $105
The area of the surface of a sphere is described by the formula S=4(3.14)r^2. The earth has a radius of 3960 miles and dry land forms 29.2% of the earth’s surface. What is the area of the dry land on earth?
Answer: [tex]57,512,581.63miles^2[/tex]
Step-by-step explanation:
Substitute the value of the radius of the Earth into the formula given in the problem, where r is the radius, to obtain the surface area of the Earth:
[tex]S=4(3.14)r^2\\S=4(3.14)(3,960miles)^2\\S=196,960,896miles^2[/tex]
The problem says that the dry land forms 29.2% of the Earth’s surface, therefore, multiply the surface area by [tex]\frac{29.2}{100}=0.292[/tex]
Threfore, the area of dry land is the following:
[tex]S_{land}=(0.292)(196,960,896miles^2)=57,512,581.63miles^2[/tex]
Final answer:
To find the area of the dry land on Earth, first, calculate the Earth's total surface area with the formula S=4(3.14)r². Given a radius of 3960 miles, this results in about 197,920,640 square miles for the total surface. Multiplying this by 29.2% (or 0.292) gives approximately 57,780,666.88 square miles of dry land.
Explanation:
The question asks for the area of the dry land on Earth, given Earth's radius and the percentage of its surface that is dry land. To find this, first calculate the total surface area of the Earth using the formula S = 4(3.14)r², where r is the radius of the Earth (3960 miles). The formula accounts for the surface area of a sphere. After calculating the total surface area, we then calculate 29.2% of this area to find the dry land's surface area.
Step-by-Step Calculation:
Calculate the total surface area of the Earth: S = 4(3.14)(3960)²
Find the area of the dry land by multiplying the total surface area by 29.2% (or 0.292).
Using the steps above:
S = 4(3.14)(3960)² = 197,920,640 square miles (approx.) as the total surface area.
Area of dry land = 197,920,640 * 0.292 = 57,780,666.88 square miles (approx.).
You read a book for 40 minutes. Then you played 3 games on the computer. Each game took 10 minutes to play. Which steps can you use to find the total number of minutes you spent reading your book and playing games?
To find the total number of minutes spent reading and playing games, add the time spent reading and the time spent playing games.
Explanation:To find the total number of minutes spent reading the book and playing games, we can add the time spent reading and the time spent playing games. First, we spent 40 minutes reading the book. Then, we played 3 games, and each game took 10 minutes to play. So, the total time spent playing games is 3 games × 10 minutes/game = 30 minutes. Finally, we can add the time spent reading and the time spent playing games: 40 minutes + 30 minutes = 70 minutes.
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To find the total number of minutes spent reading the book and playing games, you can multiply the duration of reading by 1, multiply the number of games played by the duration of each game, and then add the products together. In this case, the total number of minutes would be 70.
Explanation:To find the total number of minutes spent reading the book and playing games, you can follow these steps:
Multiply the number of minutes spent reading (40) by 1.Multiply the number of games played (3) by the duration of each game (10 minutes).Add the products from step 1 and step 2 together to find the total number of minutes.In this case, the calculation would be: 40 minutes (reading) + (3 games × 10 minutes per game) = 40 + 30 = 70 minutes.
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The price x of apples varies from 20 cents to 32 cents a pound. Write an inequality that represents this situation.
The inequality is 20¢ ≤ x ≤ 32¢
What is the median of the data set?
Answer:
8.5
Step-by-step explanation:
5 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
Cross one from the left and then one from the right
5 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
8 , 8 , 8 , 8 , 9 , 9 , 9 , 10 , 10
8 , 8 , 8 , 8 , 9 , 9 , 9 , 10
8 , 8 , 8 , 9 , 9 , 9 , 10
8 , 8 , 8 , 9 , 9 , 9
8 , 8 , 9 , 9 , 9
8 , 8 , 9 , 9
8 , 9 , 9
8 , 9
Since you have 2 numbers left, find the number right inbetween the two
Answer is provided in image attached.
Find the population of beetles a week later by first finding 6% of 350 and adding it to the original population
Step-by-step explanation:
6 percent of 350 is 21. 21 plus 350 is 371, therefore the answer is 371.
Brainliest? :)
The population of beetles a week later is 371.
The calculation is as follows:= 6% of 350 + 350
= 21 + 350
= 371
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a packer puts 50 vitamin capsules into a bottle. How many bottles are needed to pack 100 dozen capsules?
Odpowiedź
24
100. 12=1200
1200:50=24
How to do whole number between
ANSWER:
2 and 1/4
Step-by-step explanation: