Answer:
A)25% B)Product B
Step-by-step explanation:
A) To find whether product A price is increasing or decreasing, we will find the difference in price between year 0 and 1 year after.
When x = 0,
f(0) [tex]72(1.25)^{0}\\= 72*1\\= 72[/tex]
when x = 1,
f(1) = [tex]72(1.25)^{1}\\= 72*1.25\\= 90[/tex]
From here we can already see the price is increasing.
% increase = (Difference in price / Original Price) * 100
= [tex]\frac{90-72}{72} *100\\=\frac{18}{72} *100\\=0.25*100\\=25percent[/tex]
Therefore the price is increasing by 25% per year.
B) Same concept as Part A, we will find the price difference between year 1 and 2.
% increase = (Difference in price / Original Price) * 100
[tex]\frac{84.5-65}{65} * 100\\= \frac{19.5}{65} * 100\\= 0.3*100\\= 30 percent[/tex]
Therefore we can see here Product B has a higher increase than Product A.
Step-by-step explanation:
A
f(x) = 72 × 1.25 × x
so, the price is $90 after 1 year (72×1.25×1).
$180 after 2 years (72×1.25×2)
$270 after 3 years (72×1.25×3)
and so on.
or did you mean
f(x) = 72 × (1.25)^x
so, still, the price is $90 after 1 year (72×1.25^1).
$112.50 after 2 years (72×1.25^2).
$140.625 = $140.63 after 3 years (72×1.25^3)
that makes more sense. I will continue with that assumption.
so, the price is increasing, as every factor of the multiplication is positive and larger than 1. therefore, it only goes up.
and due to the formula, the price of every year is the price of the previous year multiplied by 1.25.
a multiplication by 1.25 is an increase of 25% (compared to a constant multiplication by 1).
so, the price increases every year by 25%.
B
year 1
price $65
year 2
price $84.50 difference $19.50
100% = 65
1% = 65/100 = 0.65
19.5/0.65 = 30% difference
year 3
price $109.85 difference $25.35
100% = 84.5
1% = 84.5/100 = 0.845
25.35/0.845 = 30% difference
year 4
price $142.81 difference $32.96
100% = 109.85
1% = 109.85/100 = 1.0985
32.96/1.0985 = 30% difference
so, product B has the greater percentage increase in the price (30% vs. 25%).
You need to invest $1000 in a bank account and are give two options. The first option is to earn $50 every month you leave the money in the account. The second one is to earn 3% interest each month. Describe each of these two functions and make a table of values for each for several months. Which account would you choose?
Answer:
Option 1Earn $50 every month.
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 50x + 1000[/tex]
This is a linear function.
Option 2Earn 3% interest each month.
(Assuming the interest earned each month is compounding interest.)
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 1000(1.03)^x[/tex]
This is an exponential function.
Table of values[tex]\large \begin{array}{| c | l | l |}\cline{1-3} & \multicolumn{2}{|c|}{\sf Account\:Balance} \\ \cline{1-3} & \sf Option\:1 & \sf Option\:2 \\\sf Month & \sf \$50\:per\:mth & \sf 3\%\:per\:mth \\\cline{1-3} 0 & \$1000 & \$1000 \\\cline{1-3} 1 & \$1050 & \$1030 \\\cline{1-3} 2 & \$1100 & \$1060.90 \\\cline{1-3} 3 & \$1150 & \$1092.73 \\\cline{1-3} 4 & \$1200 & \$1125.51 \\\cline{1-3} 5 & \$1250 & \$1159.27 \\\cline{1-3} 6 & \$1300 & \$1194.05 \\\cline{1-3} 7 & \$1350 & \$1229.87 \\\cline{1-3}\end{array}[/tex]
From the table of values, it appears that Account Option 1 is the best choice, as the accumulative growth of this account is higher than the other account option.
However, there will be a point in time when Account Option 2 starts accruing more than Account Option 2 each month. To find this, graph the two functions and find the point of intersection.
From the attached graph, Account Option 1 accrues more until month 32. From month 33, Account Option 2 accrues more in the account.
ConclusionIf the money is going to be invested for less than 33 months then Account Option 1 is the better choice. However, if the money is going to be invested for 33 months or more, then Account Option 2 is the better choice.
Blank + -5 = -63................................
Answer:
-58
Step-by-step explanation:
x + -5 = -63
x = -63+(-5)
x =- 58
How many solutions are there to the equation?
2x + 3 = 2x + 7
Answer:
this equation has no solutions.
Step-by-step explanation:
2x+3 = 2x+7
3=7
Find the area of the complex figure
(HELP FAST) I need help with this geometry question
Answer: no
Step-by-step explanation:
The ratio of the shorter sides is 27/5, which is equal to 3.4.
The ratio of the longer sides is 78/9, which is about 8.7.
Since the ratio of the longer sides is not equal to the ratio of the shorter sides, it is not a dilation.
Triangle ABC is an isosceles right triangle. What is the measure of one base angle?
Answer:
45°
Step-by-step explanation:
ΔABC is an isosceles right triangle. So, one angle is 90°
In an isosceles triangle, base angles are congruent.
Let the base angles be x ,x
x + x +90 = 180 {Angle sum property}
2x + 90 = 180
2x = 180 - 90
2x = 90
x = 90/2
x = 45
Base angle = 45°
Decide whether the data in the table represent a linear function or an
exponential function. Explain how you know.
y
1
16
2
8
3
0
4
-8
5
-16
A. The data represent an exponential function because there is a
common ratio of 2.
B. The data represent a linear function because there is a common
difference of 8.
OC. The data represent a linear function because there is a common
difference of -8.
D. The data represent an exponential function because there is a
common ratio of 1
Answer:
A data represent an exponential function because there is a common ratio of 1
Kyle recorded his height, in inches, from age 6 to age 18. The graph below shows the data that he recorded as a function of his height over time. Kyle plotted many of the points from memory, but has some accurate data from old medical records. His two most accurately plotted points occurred at age 6 with a height of 45 inches and at age 18 with a height of 75 inches. Use these two data points to determine the equation for the line of best fit for Kyle's data.
Answer:
you probably moved on, but for everyone else:
y= 5/2x + 30
Step-by-step explanation:
Are the two triangles similar? How do you know? (image attached)
Answer:
no
Step-by-step explanation:
they're not same because no angles are mentioned and sides are diff too
can someone do this for me please?! Just the answer pls
Answer:
see the attachment photo!
what is the polar coordinate of (0, pie)
Answer:
The angle's beginning and ending points are referred to as the initial and terminal sides, respectively. Distance from the origin and two angles are the three parameters of 3D polar coordinates or spherical coordinates. is a three-dimensional polar coordinate.
Step-by-step explanation:
Read above.
Identify the angle of depression.
Answer:
4
Step-by-step explanation:
An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line.
An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line.
∠3 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
∠4 is an angle of depression because it is formed by the line of sight that is below the horizontal line.
∠5 is neither an angle of depression nor an angle of elevation because it is not formed by the horizontal line and the line of sight.
∠6 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
Therefore, the angle of depression is ∠4.
combine like terms to simplify 3x + 5 - 2x
Step-by-step explanation:
3x and 2x are like terms so,
3x + 5 - 2x
3x - 2x + 5 = x + 5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression
[tex]\star~~\large\pmb{3x+5-2x}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Combine like terms.The like terms here are: 3x-2x; let's combine them:
[tex]\star~\large\pmb{x+5}[/tex]
We can't simplify this any further, because x and 5 are not like terms.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{Variables\:and\;numbers\;are\;not\;like\;terms}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
If you rolled two dice, what is the probability
that you would roll a sum of 4?
Give your answer as a simplified fraction.
Answer:
1/36.
Step-by-step explanation:
A total number of possible outcomes = 36.
To get a sum of 12 the possible outcomes are just 6,6.
unit rate for typing 34 words in a minute in a half
Answer:
Rate is 1.1333 words per second
Step-by-step explanation:
We understand rating as frequency or speed of doing something per time (seconds mainly)
[tex]{ \green{ \tt{rate = \frac{item \: quantity}{time} }}} \\ [/tex]
Let's find rate in terms of seconds (words per second)
[tex]{ \rm{rate = \frac{34 \: words}{ (\frac{1}{2} \times 60) \: seconds} }} \\ \\ { \rm{rate = \frac{34}{30} }} \\ \\ { \rm{rate = 1.133 \: \: words \: per \: second}}[/tex]
After years of successful existence, a company producing Smart TV formulated an equation for the cost P of manufacturing n number of television sets. The equation is P(n)=1200n+700. Find the cost of 50 television set.
a. Php 59,300
b. Php 60,000
c. Php 60,700
d. Php 61,200
Put n=50
P(50)
1200(50)+70060000+70060700Option C
Answer:
C
Step-by-step explanation:
To find the cost for 50 televisions:
We put the value of n=50
P(50)
1200(50)+700
60000+700
60, 700
Option C
If f(x)=(4x-3) / 2 and g(x) =(2x+3) / 4, which of the following is true?
A f(g(x)) =1
B f(g (x)) = 0
C f(g(x))=-1
D f(g(x)) = x
Answer:
f(g(x))= x
Step-by-step explanation:
f(x)=(4x-3)/2
g(x) =(2x+3)/4
f(g(x)) means use the value obtained from g(x) in the equation defined by f(x). Since g(x) =(2x+3)/4, we can substitute (2x+3)/4 in place of the x in f(x).
If f(x)=(4x-3)/2 then use the expression (2x+3)/4 in place of "x" in (4x-3)/2
f(x) = (4x-3)/2
g(x) = (2x+3)/4
f(g(x))=(4((2x+3)/4)-3)/2
f(g(x))=(((8x+12)/4)-3)/2
f(g(x))= (2x+3-3)/2
f(g(x))= 2x/2
f(g(x))= x
i been asking for help since yesterday
Use the graph above to complete problems 1 - 5.
Mary is planning a costume party. She spent $375.00 as shown on the graph. How much of the money was spent, to the nearest dollar, on the following items?
1) On decorations?
2) On food?
3) On party hall rental?
4) On prizes?
5) On invitations?
solve x - 23 = 57 ⅔ x = 7
Step-by-step explanation:
[tex]x - 23 = 57 \\ x = 57 + 23 \\ x =80 \\ \\ \frac{2}{3}x = 7 \\ ( \frac{3}{2}) \frac{2}{3}x = 7( \frac{3}{2}) \\ x = \frac{21}{2} [/tex]
Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
More about equation of line :
brainly.com/question/14200719
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Let R be the region in the first quadrant enclosed by the graph y=(square root(6x+4)), the line y=2x, and the y-axis. . . .Set up but do not integrate an integral,expression in terms of a single variable for the volume of the solid generated when R is revolved about the y axis
The two boundary curves y = √(6x + 4) and y = 2x meet at
√(6x + 4) = 2x
6x + 4 = 4x²
2x² - 3x - 2 = 0
(x - 2) (2x + 1) = 0
⇒ x = -1/2 and x = 2
R is bounded to the left by the y-axis (x = 0), so R is the set
R = {(x, y) : 0 ≤ x ≤ 2 and 2x ≤ y ≤ √(6x + 4)}
Using the shell method, the volume is made up of cylindrical shells of radius x and height √(6x + 4) - 2x. So each shell of thickness ∆x contributes a volume of
2π (radius) (height) ∆x = 2π x (√(6x + 4) - 2x) ∆x
and as we let ∆x approach zero, the total volume of the solid is given by the definite integral
[tex]\displaystyle \boxed{2\pi \int_0^2 x \left(\sqrt{6x + 4} - 2x\right) \, dx}[/tex]
2. Use the figures below for parts a through c.
B
45°
15
90% C
105°
120%
105°
W
80
(a) Are the corresponding angles in figures ABCD and WXYZ congruent? (1 pt)
Circle or highlight one:
Yes
No
(b) Are the corresponding sides in figures ABCD and WXYZ proportional? (1 pt)
Circle or highlight one:
Yes
No
Show your work for part b below. (2 pts)
(c) Are figures ABCD and WXYZ similar? (1 pt)
Circle or highlight one:
Yes
45°
No
110
150
120%
Z
90% Y
40
Answer:
see the attachment photo!
This Week's High Temperatures (°F)
29, 38, 45, 31, 50, 58, 62
Last Week's High Temperatures (°F)
44, 31, 66, 32, 26, 58, 78
Which measures of center and variability for the
temperatures were lower this week than last week?
Check all that apply.
mean
median
mode
range
mean absolute deviation
Done
The measures of center and variability for the
temperatures that were lower this week than last week include mean, range, mean absolute deviation.
What is a mean?It should be noted that a mean simply means the average set if numbers given.
Also, the range is the difference between the highest number and the lowest number in the data.
Learn more about mean on:
brainly.com/question/1136789
#SPJ1
Answer:
mean,range,mean absolute deviation
Step-by-step explanation:
just took it on edge
Zack has 2 feet of balsa wood. he needs twice that amount to finish a project. the cost is $0.05 per inch. how much will the balsa wood cost zack.
Answer:
$1.2
Step-by-step explanation:
There is 12 inches in a foot, and if he needs twice the amount he already has which is 4 then you would multiply 0.05 times 24 and you would get $1.2
Answer: $1.20 for 2 feet of balsa wood
Step-by-step explanation: There are 12 inches in 1 foot, and 24 inches in 2 feet. The cost per inch is 0.05, multiplying 24 (inches) x 0.05 (the cost per inch) would equal $1.20
please help I need this done today
Answer: 45 degrees
Step-by-step explanation:
90-45 = 45
A certain planet has a day length of 24 hours. the planet is totally covered in water,
except for one small island. at hour 0, the island has 100% light with the planet's star
in the top of the sky. at hour 12, the island has 0% light and is in total darkness.
write an equation that models the amount of light in the sky on the island in terms
of hours passed.
Answer:
above
Step-by-step explanation:
the entire method for the question is linked above :)
PLEASE HELP!!! find the area of the shaded triangle
Answer:
4 ft squared
Step-by-step explanation:
2 add 2 is 4
4 multiplied by 4 is 16
16 divided by 2 is 8
8 divided by 2 is 4
Which is not a function?
Can give brainliest!!
Answer:
Number #1
Step-by-step explanation:
#1 isn't a function
Answer:
Choice 3 is not a function.
Step-by-step explanation:
Reason: It has points (1,3) and (1,7). X cannot repeat otherwise it is not a function.
Hope this helps!
If not, I am sorry.
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−3/4x, through (4, -1)
Answer:
y = -3/4x + 2
Step-by-step explanation:
The line is parallel to y = -3/4x and passes through the point (4, -1)
=============================================================
Solving :
⇒ As they are parallel, the slope remains the same (-3/4)
Now apply into the point slope formula :
⇒ y + 1 = -3/4 (x - 4)
⇒ y + 1 = -3/4x + 3
⇒ y = -3/4x + 2 [in slope-intercept form]
does someone mind helping me with this question? Thank you!
Answer:
60
Step-by-step explanation:
Use PEMDAS (parentheses, exponent, multiply, divide, addition, subtraction)
First, substitute 5 for x:
3(3(5) + 5)
Multipliy inside the parentheses:
3(15 + 5)
Add inside the parentheses:
3(20)
Multiply:
60
There's your answer! Hope I helped.