Answer:
Part A) The reasonable domain to plot the growth function is the interval [0,5]
Part B) The average rate of change is [tex]0.21\ \frac{cm}{day}[/tex]
see the explanation
Step-by-step explanation:
Part A)
Let
f(n) -----> the height of the plant in cm
n ----> the number of days
we have
[tex]f(n)=10(1.02)^n[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^x[/tex]
where
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
In this problem we have
[tex]a=10\ cm[/tex] ----> initial value or y-intercept
[tex]b=1.02\\r=b-1=1.02-1=0.02\\r=2\%[/tex]
For f(n)=11.04 cm
Find the value of n
substitute in the exponential function
[tex]11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n[/tex]
Apply log both sides
[tex]log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days[/tex]
so
The reasonable domain to plot the growth function is the interval -----> [0,5]
[tex]0 \leq x \leq 5[/tex]
Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?
the average rate of change is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]f(a)=f(1)=10(1.02)^1=10.2\ cm f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\[/tex]
Substitute
[tex]\frac{11.04-10.2}{5-1}=0.21\ \frac{cm}{day}[/tex]
The average rate of change is the change of the function values (output values) divided by the change of the input values.
That represent ----> The plant grew an average of 0.21 cm per day during that time interval
"Part A) The reasonable domain to plot the growth function is the interval [0,5]
Part B) The average rate of change is
see the explanation
Step-by-step explanation:
Part A)
Let
f(n) -----> the height of the plant in cm
n ----> the number of days
we have
This is a exponential function of the form
where
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
In this problem we have
----> initial value or y-intercept
For f(n)=11.04 cm
Find the value of n
substitute in the exponential function
Apply log both sides
so
The reasonable domain to plot the growth function is the interval -----> [0,5]
Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?
the average rate of change is equal to
In this problem we have
Substitute
The average rate of change is the change of the function values (output values) divided by the change of the input values.
That represent ----> The plant grew an average of 0.21 cm per day during that time interval"quoted from
"calculista"
How long is a guy wire reaching from the top of a 6ft. Pole to a point on the ground 4ft. From the pole
Answer:
the guy wire is 7.211 ft long
Step-by-step explanation:
Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.
Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:
[tex]Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft[/tex]
Plz help I dont know this answer do if u can help plz do
Answer:
The scale factor is 1/3
Step-by-step explanation:
we know that
The scale factor is equal to divide the length side of the image (square A'B'C'D') by the length side of the pre-image (square ABCD)
Let
z ---> the scale factor
x----> the length side of the image (square AB'C'D')
y----> the length side of the pre-image (square ABCD)
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=2\ units\\y=6\ units[/tex]
substitute
[tex]z=\frac{2}{6}[/tex]
simplify
[tex]z=\frac{1}{3}[/tex]
The scale factor is less than 1, so the dilation is a reduction
therefore
The scale factor is 1/3
The area of a rectangular tennis court is 140 square meters. It’s length is 6 meters less than twice it’s width. Find the dimensions of the tennis court
The dimensions of the tennis court are:
Length = 14 m
Length = 14 mWidth = 10 m
Let the width be y.
From the question given above,
The length is 6 meters less than twice it’s width. This can be obtained written as:
Length = 2y – 6Area = 140 m²
Dimension =? Next, we shall determine the width (i.e y)Dimension = Area = Length × width
140 = (2y – 6)y
140 = 2y² – 6y
Rearrange
2y² – 6y – 140 = 0
Divide through by 2
y² – 3y – 70 = 0
Multiply the 1st term (i.e y²) and the last term (i.e –70) together. The result is –70y². Find two factors of –70y² such that their sum will result to the 2nd term (i.e –3y). The factors are –10y and 7y.Substitute –10y and 7y in place of –3 in the equation above.y² – 3y – 70 = 0
y² – 10y + 7y – 70 = 0
Factorize
y(y – 10) + 7(y – 10) = 0
(y – 10)(y + 7) = 0
y – 10 = 0 or y + 7 = 0
y = 10 or –7
Since measurement can not be negative,
Width = y = 10 m
Finally, we shall determine the length.Length = 2y – 6
y = 10
Length = 2(10) – 6 = 20 – 6
Length = 14 mTherefore, the dimensions of the tennis court are
Length = 14 m
Length = 14 mWidth = 10 m
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One of the zookeepers solved to find Bernard’s speed when he is healthy using the equation:
x – 41.5 = 13.5.
The other zookeeper said that to solve for Bernard’s speed when he is healthy, they must use the equation: 41.5 + 13.5 = x.
Which zookeeper is correct? Explain.
Answer:
Both the zoo-keepers are correct.
Step-by-step explanation:
The first zoo keeper uses the equation:
x - 41.5 = 13.5
⇒ x = 13.5 + 14. 5 = 55
Now, the second zoo- keeper uses the equation:
41.5 + 13.5 = x
⇒ x = 55
Both use x = 55.
Answer:
Both zookeepers are correct because they have equivalent equations. Both of the equations will give a healthy speed of 55 km/hr
Step-by-step explanation:
examples response
A 50% increase followed by a 33.33% decrease
Answer:
Greater than the original value because it increases is more than the decrease
Step-by-step explanation:
Answer:
Overall, a 200% increase.
Step-by-step explanation:
Quantity after a 50% increase would be 1.50x, where x is the starting value.
if a 33.33% increase were to follow, then the final quantity would be
1.3333(1.50x), or just barely under 2x (representing an increase of 200% in x).
can someone help me please do tomorrow
Answer:
B
Step-by-step explanation:
Square root of 72=
8.485281474
A. 6
B. 6 square root 2=
8.485281474
C. 36
D. square root of 6=
2.449489743
Suppose yoko borrows $3500 at an interest rate of 4% compounded each year Find the amount owed at the end of 1 year
Amount owed at the end of 1 year is 3640
Solution:Given that yoko borrows $3500.
Rate of interest charged is 4% compounded each year
Need to determine amount owed at the end of 1 year.
In our case :
Borrowed Amount that is principal P = $3500
Rate of interest r = 4%
Duration = 1 year and as it is compounded yearly, number of times interest calculated in 1 year n = 1
Formula for Amount of compounded yearly is as follows:
[tex]A=p\left(1+\frac{r}{100}\right)^{n}[/tex]
Where "p" is the principal
"r" is the rate of interest
"n" is the number of years
Substituting the values in above formula we get
[tex]\mathrm{A}=3500\left(1+\frac{4}{100}\right)^{1}[/tex]
[tex]\begin{array}{l}{A=\frac{3500 \times 104}{100}} \\\\ {A=35 \times 104} \\\\ {A=3640}\end{array}[/tex]
Hence amount owed at the end of 1 year is 3640
1) There are 16 rows of chairs in the auditorium. Each row has the same
number of chairs. There are 512 chairs in all. How many chairs in each row?
Answer:
32 chairs in each row
The drawing will help.
To find out how many chairs are in each row, divide the total number of chairs by the number of rows. In this case, there are 16 rows and 512 chairs in total, so there are 32 chairs in each row.
Explanation:To find out how many chairs are in each row, you need to divide the total number of chairs by the number of rows. In this case, there are 16 rows and 512 chairs in total. So, you can divide 512 by 16 to find out how many chairs are in each row. The result is 32. Therefore, there are 32 chairs in each row of the auditorium.
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Determine the values of k and p so that the solution is “All Reals” when solving for y:
81y - 17 = k2y + 6+p
Answer:
[tex]k=\pm9,p=-23[/tex]
Step-by-step explanation:
Given:
The equation is:
[tex]81y - 17 = k^2y + 6+p[/tex]
Here, the left hand side of the equation will be equal to that of the right hand side only if the coefficients of 'y' are same on both sides and the constant terms are also equal to each other.
Therefore,
[tex]81=k^2\ and\ -17=6+p[/tex]
Solving each for 'k' and 'p'.
[tex]k^2=81\\\textrm{Taking square root on both the sides}\\\sqrt{k^2}=\pm\sqrt{81}\\k=\pm9.......(\sqrt{81}=9)[/tex]
[tex]-17=6+p\\\textrm{Adding -6 on both the sides}\\-17-6=p+6-6\\p=-23[/tex]
Therefore, the values of 'k' are -9 and 9. Value of 'p' is -23.
Is the following relation a function?
Answer:
NoStep-by-step explanation:
A function is a relation between sets that associates to every element of a first set exactly one element of the second set.
Each element from the first set is assigned exactly one element from the second set.
It's not a function, because for 0 are assigned two elements 1 and 3.
Vi walks five days each week.She walks the same distance on the first two days.On days three and four,Vi walks twice as long as on the first two days.On day five she walks half as far as on day 1.If Vi walks 13 miles each week how does she walk each day
Vi walks 2 miles on first day, 2 miles on second day, 8 miles on third and fourth day and 1 mile on fifth day.
Step-by-step explanation:
Let,
x be the distance walked by Vi.
Therefore,
On first day = x
Second day = x
On days three and four,Vi walks twice as long as on the first two days
Third and fourth day = 2(x+x) = 2(2x) = 4x
On fifth day = half of first day = [tex]\frac{1}{2}x[/tex] = 0.5x
Total distance = 13 miles
Therefore,
[tex]x+x+4x+0.5x =13\\6.5x=13[/tex]
Dividing both sides by 6.5
[tex]\frac{6.5x}{6.5}=\frac{13}{6.5}\\x=2[/tex]
Distance on first day = x = 2 miles
second day = x = 2 miles
third and fourth day = 4x = 4(2) = 8 miles
fifth day = 0.5x = 0.5(2) = 1 miles
Vi walks 2 miles on first day, 2 miles on second day, 8 miles on third and fourth day and 1 mile on fifth day.
Keywords: distance, addition
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14. A recipe calls for % cup brown sugar for
(each 2/3 cup white sugar. How many cups of
brown sugar per cup of white sugar is this?
(green)
Answer:
1 1/8 cup of brown sugar.
Step-by-step explanation:
Here is the correct question: A recipe calls for 3/4 cup brown sugar for each 2/3 cup white sugar. How many cups of brown sugar per cup of white sugar is this?
Given: 3/4 cup of brown sugar for each 2/3 cup of white sugar.
Finding requirement of brown sugar for 1 cup of white sugar.
∴ Each 2/3 cup of white sugar require 3/4 cup of brown sugar.
Now, 1 cup of white sugar require brown sugar = [tex]\frac{\frac{3}{4} }{\frac{2}{3} } cups[/tex]
= [tex]\frac{3}{4} \times \frac{3}{2} = \frac{9}{8} \ cup[/tex]
Thus, we can say [tex]\frac{9}{8}[/tex] = 1 1/8 cup of brown sugar is required per cup of white sugar.
Mr. Davis purchased fifty $1,000 bonds at 96.50. The annual interest rate is 8.5%. Find the amount of each semi-annual interest payment.
$4,250
$2,125
$1,062.50
$3,354.75
None of these choices are correct.
Final answer:
The amount of each semi-annual interest payment that Mr. Davis receives for his fifty $1,000 bonds at an 8.5% annual interest rate is $2,125.
Explanation:
Mr. Davis purchased fifty $1,000 bonds at 96.50, and the annual interest rate is 8.5%.
To calculate the semi-annual interest payment on a bond, you first need to determine the annual interest amount per bond, and then divide it by two, because interest is paid semi-annually.
First, find the annual interest for a single bond: $1,000 x 0.085 = $85.
Since Mr. Davis owns 50 bonds, the total annual interest for all bonds is 50 x $85 = $4,250.
Now, to find the semi-annual interest payment, divide the total annual interest by 2:
$4,250 / 2 = $2,125.
Therefore, the amount of each semi-annual interest payment that Mr. Davis receives is $2,125.
A bicycle rental shop rents bicycles for $8 per hour. The total cost c
(in dollars) for renting a bicycle h hours is given by the function c = 8h. Once you get
to the rental shop, you figure you can rent a bicycle for at most 5 hours. What is the
most that you will pay for renting the bicycle?
The most you will pay for renting the bicycle for at most 5 hours is $40.
Explanation:The total cost of renting a bicycle for h hours is given by the function c = 8h, where c represents the total cost and h represents the number of hours rented. In this case, you figure you can rent a bicycle for at most 5 hours. To find the most that you will pay, substitute h = 5 into the function c = 8h:
c = 8(5) = 40
Therefore, the most you will pay for renting the bicycle for at most 5 hours is $40.
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Factor by grouping.
72x^3 - 56x^2 + 45x - 35
Answer:
[tex](8x^{2} +5)(9x-7)[/tex]
Step-by-step explanation:
[tex]72x^{3}-56x^2+45x-35[/tex]
Out of 72x^3 and 56x^2 you can factor 8x^2
Out of 45x and -35 you can factor 5
So if you put those together you get 8x^2+5
8x^2*9x=72x^3 and 8x^2*-7= -56x^2
5*9x=45x and 5*-7= -35
when round off to nearest thousand, the number 42,099
Answer:42000
Step-by-step explanation:
There is no number higher than 5 after the thousands so you would keep it the same
5. Kim bakes 1/4 of the cookies that are sold at a local bake sale, One-third of her cookies are
chocolate chip. One-fourth of Kim's chocolate chip cookies have nuts. Whan fraction of the
cookies at the bake sale are Kim's chocolate chip cookies with nuts?
Answer:
[tex]\frac{1}{48}[/tex]th
Step-by-step explanation:
Let X cookies are sold at the local bake sale.
So,
[tex]\frac{X}{4}[/tex] cookies will be made by Kim.
Now,
Given is One-third of her cookies are chocolate chip.
So, One-third of [tex]\frac{X}{4}[/tex] will be chocolate chip
Which is [tex]\frac{X}{12}[/tex].
Out of whixh one-fourth have nuts.
So,[tex]\frac{X}{48}[/tex] cookies will be having nuts.
So, [tex]\frac{1}{48}[/tex]th of the Total cookies at the bake (X) will be having nuts.
I NEED HELP QUICKKKKK
Tina's salsa class membership, which is $15, is deducted automatically from her bank account every month. Which expression shows the total deductions for the year?
(−$15) − 12
(−$15) + 12
(−$15) ÷ 12
(−$15) ⋅ 12
Answer:
the last one
(-15)x12
hope this helps!
Alberto has four rectangular tiles. The dimensions of the tiles, in inches, are 2 x 3, 3 x 5, 1 x 4, and 4 x 6. He puts all four tiles together, without gaps or overlaps, to form a single square. What is the side length of the square?
Answer:
The side length of the square is 7 inches².
Step-by-step explanation:
Given:
The dimensions of the tiles are 2 x 3, 3 x 5, 1 x 4, and 4 x 6 to form a single square.
Now, to get the length of the square formed by the tiles. We need to get the area of the square.
Area of the square formed by the four tiles = [tex]2\times 3+3\times 5+1\times 4+4\times 6[/tex]
= [tex]6+15+4+24[/tex]
= [tex]49[/tex]
So, the area of the square is 49 inches².
Putting the formula of square for getting the side length:
Area of the square = side²
[tex]49=side^{2}[/tex]
using square root on both sides:
[tex]7=side[/tex]
Therefore, the side length of the square is 7 inches².
helppppp pleaseeeeeee
Answer: C
Step-by-step explanation:
y<x-1
so you looking at the region below the line but not including it so graph c is good
Answer:
If you need proof here it is
Josh deposits $4000 into an account that pays simple interest at a rate of 5% per year. How much interest will he be paid in the first 4 years?
i don't know how to solve this question. Please show work!!!
Answer:4000 deposit times 0.5 interest is 2,000. 2,000 x4 = 8,000 for 4 years.
Step-by-step explanation:
A washer and dryer cost $600 combined. The cost of the washer is three times the cost of the dryer
The sum of two consecutive negative integers whose product is 156. Find the integers
Answer:
The integers are -13 and -12
Step-by-step explanation:
Let
x ----> the first consecutive negative integer
x+1 ----> the second consecutive negative integer
we know that
[tex]x(x+1)=156[/tex]
Apply the distributive property
[tex]x^2+x=156\\x^2+x-156=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^2+x-156=0[/tex]
so
[tex]a=1\\b=1\\c=-156[/tex]
substitute in the formula
[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(1)(-156)}} {2(1)}[/tex]
[tex]x=\frac{-1(+/-)\sqrt{625}} {2}[/tex]
[tex]x=\frac{-1(+/-)25} {2}[/tex]
[tex]x_1=\frac{-1(+)25} {2}=12[/tex] ----> the solution cannot be a positive number
[tex]x_1=\frac{-1(-)25} {2}=-13[/tex]
therefore
[tex]x=-13\\x+1=-12[/tex]
18) The ratio of the number of boys to the number of girls in the class is 1:6. Which statement must describe the class? A) There are exactly 7 students in the class. B) There is 1 boy for every 6 girls in the class. C) There are 5 more girls than boys in the class. D) There is 1 boy out of the 6 students in the class
Answer:
B. There is one boy for every 6 girls in class.
Step-by-step explanation:
When you have a ratio, it compares two numbers. When you have a ratio 1:6 the colon (:) there can be read as "is to" or "for every".
That means that ratio can be read as 1 is to 6 or "there is 1 for every 6."
In this case 1:6 represents the number of boys to the number of girls to class. This means that there is 1 boy for every 6 girls in class.
Answer:
choose b or d
Step-by-step explanation:
Use the chart by multiply the binomial by the trinomial. (2y+3)(3y2+4y+5)
Answer:
6y^3+17y^2+22y+15
Step-by-step explanation:
(2y+3)(3y^2+4y+5)
6y^3+8y^2+10y+9y^2+12y+15
6y^3+17y^2+22y+15
Answer:
B. 6y^3+17y^2+22y+15
Step-by-step explanation:
"71 points". Match the proportional relationships to their corresponding equations.
11 pounds of apples for $40.59
12 gallons of gasoline for $44.16
15 magazines for $54.75
14 sandwiches for $50.68
t = $3.69n
arrowBoth
t = $3.62n
arrowBoth
t = $3.65n
arrowBoth
t = $3.68n
arrowBoth
Answer:
1 pound of apples cost $3.69,
1 gallon of gasoline for $3.68,
1 magazine for $3.65,
1 sandwich for $3.62.
Step-by-step explanation:
40.59/11=3.69
44.16/12=3.68
54.75/15=3.65
50.68/14=3.62
11 pounds of apples for $40.59 Equation: t = $3.69n. 12 gallons of gasoline for $44.16 Equation: t = $3.68n. 15 magazines for $54.75 Equation: t = $3.65n. 14 sandwiches for $50.68 Equation: t = $3.62n with arrowBoth.
To match the proportional relationships to their corresponding equations:
1. 11 pounds of apples for $40.59
- The cost per pound is [tex]\( \frac{40.59}{11} \approx 3.69 \).[/tex]
- Equation: t = $3.69n
2. 12 gallons of gasoline for $44.16
- The cost per gallon is [tex]\( \frac{44.16}{12} \approx 3.68 \).[/tex]
- Equation: t = $3.68n
3. 15 magazines for $54.75
- The cost per magazine is [tex]\( \frac{54.75}{15} \approx 3.65 \).[/tex]
- Equation: t = $3.65n
4. 14 sandwiches for $50.68
- The cost per sandwich is [tex]\( \frac{50.68}{14} \approx 3.62 \).[/tex]
- Equation: t = $3.62n
In each case, the equation t = kn represents the proportional relationship, where k is the constant unit rate of cost per item. The arrowBoth indicates the direction of the proportional relationship.
Use 4 fours to make 2
Answer:
4/2=2
Step-by-step explanation:
Step-by-step explanation:
4/4 + 4/4
1 + 1
2
Which expression is equal to (2x − 2)(3x – 3)?
6x2 - 12x +6
5x2 - 6x-5
6x2 – 123 - 5
6x2 + 12x - 6
Answer:
6x^2-12x+6
Step-by-step explanation:
(2x-2)(3x-3)
6x^2-6x-6x+6
6x^2-12x+6
The product of (2x - 2) and (3x - 3) using the FOIL method is 6x^2 - 12x + 6.
Explanation:The expression (2x − 2)(3x – 3) can be considered as a product of two binomials and can be solved by applying the distributive property or the FOIL method - First, Outer, Inner, Last. We first distribute the 2x from the first binomial to each term in the second binomial (6x2 - 6x) and do the same with -2 (-6x + 6). Adding these together leads to 6x2 - 12x + 6, which is none of the options provided.
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The stem and leaf plot shows high temperatures
recorded each day at the beginning of the month.
Which temperature occurs the most frequently?
degrees
During how many days was the high in the 70s?
days
Answer: 54 Degrees, 2days
Step-by-step explanation:
Answer:
54 Degrees, 2days
Step-by-step explanation:
If you bought a stock last year for a price of $36, and it has gone down 16.6% since then, how much is the stock worth now, to the nearest cent?
Answer:
The stock is now worth of $30.024.
Step-by-step explanation:
Here, the price of the stock last year =$36
The percentage down in the price of stock in a year = 16.6 %
Now, 16.6% of the value of stock $36 = [tex]\frac{16.6}{100} \times 36= 5.976[/tex]
⇒16.6% of $36 = $ 5.976
Now, the Current Worth of Stock = Stock Value last year - Decrease in the stock price
= $36 - $ 5.976 = $30.024
Hence, the stock is now worth of $30.024.