Answer:
[tex]y= 500(1+0.15)^x[/tex]
Step-by-step explanation:
This problem can be solved using concept of compound interest
In compound interest
if p is the principal amount
and r is the interest rate
then value of principal amount(A) after n years time is given by
A = p(1+r)^n
=>[tex]A = p(1+r)^n[/tex]
__________________________________
in the problem
in place of n we have x years
y is the amount which is the total amount after n years
p is the principal money deposited = $500
r = 15%
substituting these value in the formula for amount after n years we have
[tex]y= 500(1+15/100)^x\\y= 500(1+0.15)^x[/tex]
Thus, function modeling the situation is [tex]y= 500(1+0.15)^x[/tex]
HELP!!!! Identify the volume of the composite figure rounded to the nearest tenth.
Answer:
4618.1 ft³
Step-by-step explanation:
Volume of the cone:
[tex]V_{cone} = \frac13 \pi r^2 h[/tex]
[tex]V_{cone} = \frac13 \cdot \pi \cdot 49 \cdot 12 = 196\pi[/tex]
Volume of the cilinder:
[tex]V_{cilinder} = \pi r^2 h[/tex]
[tex]V_{cilinder} = \pi \cdot 49 \cdot 22 = 1078\pi[/tex]
Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) + 1.
Answer:
Step-by-step explanation:
A quadrilateral has all sides and angles congruent. Which name best describes the figure? a. rhombus b. square c. rectangle d. trapezoid
Answer:
It's a square
Step-by-step explanation:
Because a square has all equal sides, and its an quadrilateral, and we know its square bc the other shapes dont really have that.
The square is also the name of the regular quadrilateral — one in which all sides are congruent and all angles are congruent.
On a shelf there are 6 novels, 8 poetry books, and 4 mystery books. What is the probability that person A chooses a novel,then a mystery and walks away, then person B picks a mystery and a poetry book?
Answer:
2/255
Step-by-step explanation:
In total, there are 18 books on the shelf.
The probability that person A will pick a novel is 6/18 = 1/3
There are now 5 novels and 17 total books on the shelf
The probability that person A then picks a mystery is 4/17.
There are now 3 mysteries and 16 total books on the shelf.
The probability that person B then picks a mystery is 3/16.
There are now 2 mysteries and 15 total books on the shelf.
The probability that person B then picks a poetry book is 8/15.
The probability that all these events occur back to back is the product of their individual probabilities. Therefore, the probability is:
1/3 * 4/17 * 3/16 * 8/15 = 2/255
someone pls help me with this :nth term of 3 4.5 6 7.5 I need the answer asap
Answer:
9.5
Step-by-step explanation:
the numbers go up by 1.5
so, 7.5 + 1.5 = 9
convert 55/100 to a decimal, please
Answer:0.55
Step-by-step explanation:
OK decimal means one number before (.) (point)
for example if question is
1.) 55/10 = ans: 5.5 (here before . (point) 5 is there only one number
2.)55/1000= ans: 0.055(here before .(point) 0 is there only one number
3.)like ur question 55/100= 0.55 ☻
Answer: 0.55
Step-by-step explanation:
Because 55/100 is 55% and 55% in decimal form is .55. Always move the decimal to the right when the percentage is under 100%.
Simplify 12 square root of 7
Answer:
Step-by-step explanation:
[tex]12\sqrt{7}\\=31.74901[/tex]
A water grist mill has a radius of 8ft and takes 6 seconds to make a complete rotation. A bucket starts at position (8,0). What are the coordinates of the bucket's location after 4 seconds? Round values to the nearest tenth.
(8.7, −3.5)
(−4, −6.9)
(4, −6.9)
(−8.7, −3.5)
Answer:
(−4 -6.9 )= x, y rotation 240 degree anti clockwise
Step-by-step explanation:
We are told radius = 8 so the center point or point of origin is 0.0
360/3 = 120 degree x 2 = 240 degree is where we need to be.
(8,0) circulating anti clockwise = -8,0 at 180 = 180 degree.
This is 3 seconds.
We divide 8/3 to find the 4th and know it will be negative in the 3rd quadrant across the negative y axis, the lower and left point on the graph.
We know both are negative if going anti clockwise 240 degree.
We also know that the hands of a clock or mechanics of a mill cannot increase in length they shorten so they cannot be 8.7 even though triangles slants do increase this is independent of completing the lengths in a triangle. The lengths shorten.
-4 = x this is because it crosses -4 x axis to reach to -6.9 y coordinate.
Y= 6.9 as the length of 8 is shortened by 1.1 units between each 180 degree line we have 210deg (shows (-6.35, -2.4) also; 240 deg (-6.9, -4 ) and a 270 deg (this shows (0,8)
if 240/6.9 = 34% reduction
As 8 6.9 of 8 as a percentage = 86.25
As a ratio decrease we have 13.75% with the size of the coordinates at 240 degrees from 180 degrees the highest point is 270 degrees and is half again 1.1/2 = 0.55 increase in coordinates of y.
y would show -6.35 at 210 degrees and x would show 1.1 whole ratio change and show -2.4 at 210 degrees. The reason for this is that it is cutting the axis line and is a narrowing crossing for x axis shortly before 180 degree change.
The shortest point of the hand and central to 240 and 180 is 210 degree.
6x-2x+8y-6y (algebra answr very urgent
The solution to the expression 6x - 2x + 8y - 6y is 4x + 2y
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
6x - 2x + 8y - 6y
Collect the like terms in the expression
So, we have the following representation
6x - 2x + 8y - 6y = 6x - 2x + 8y - 6y
Evaluate the like terms in the expression
So, we have the following representation
6x - 2x + 8y - 6y = 4x + 2y
Hence, the simplified expression is 4x + 2y
Read more about expressions at
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11. Michael is trying to rent a car during his vacation. He finds two companies
with the following deals.
Carol's Car Rentals
AL's Auto Rentals
$180 down payment
+ $15 per day
$250 down payment
$s per day
+
Part A: Write an expression that represents the cost at Carol's Car Rentals for (d)
days.
Your answer
Answer:
$180 + $15d
Step-by-step explanation:
Since Carol's Car Rentals offers a deal of $180 down payment + $15 per day and AL's Auto Rentals offer a deal of $250 down payment $5 per day. To calculate the cost of Carol's Car Rentals deal, we use the formula:
cost of Carol's Car Rentals = Down payment + cost per day.
If you are to rent at Carol's Car Rentals for d days; The cost of Carol's Car Rentals = Down payment + cost per day = $180 + $15 per day × d days
cost of Carol's Car Rentals = $180 + $15d
Help help help help please please
Answer:
The answer is 10⁴ × 4⁵.
Step-by-step explanation:
First, you can seperate the fraction :
[tex] \frac{ {10}^{4} \times {4}^{10} }{ {4}^{5} } [/tex]
[tex] = {10}^{4} \times \frac{ {4}^{10} }{ {4}^{5} } [/tex]
Next, you have to apply Indices law :
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
So for this question :
[tex] {10}^{4} \times \frac{ {4}^{10} }{ {4}^{5} } [/tex]
[tex] = {10}^{4} \times {4}^{10 - 5} [/tex]
[tex] = {10}^{4} \times {4}^{5} [/tex]
If f(x)=x^2+1 and g(x) = x-4 which value is equivalent to (f•g)(10)
Which table represents the graph of a logarithmic function in the form y=log3x when b>1?
Answer:
The satisfied table of the given function[tex]y = log_{b} (x)[/tex]
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
Step-by-step explanation:
Explanation :-
Given logarithmic function [tex]y = log_{b} (x)[/tex] if b >1
Given first table
i)
put x = [tex]\frac{1}{8}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{8} )[/tex]
[tex]y = log_{2} (2^{-3} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3[/tex]
y = -3
ii)
put x = [tex]\frac{1}{4}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{4} )[/tex]
[tex]y = log_{2} (2^{-2} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2[/tex]
y = -2
iii)
put x = [tex]\frac{1}{2}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{2} )[/tex]
[tex]y = log_{2} (2^{-1} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1[/tex]
y = -1
iv)
put x = 1 given b > 1 so we can choose b = 2
[tex]y = log_{2} (1 )[/tex] = 0
y = 0
v)
put x = [tex]2[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (2 )[/tex]
y = 1
Final answer:-
The satisfied table of the given function
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
The first option is correct because that table of values represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Given:
The lograrithmic function form is [tex]y=\log_b x,b>1[/tex].
To find:
The table of values that represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Explanation:
It is given that [tex]b>1[/tex]. Let [tex]b=2[/tex], then
[tex]y=\log_2 x[/tex] ...(i)
Substitute [tex]x=\dfrac{1}{8}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{8}[/tex]
[tex]y=\log_2 \dfrac{1}{2^3}[/tex]
[tex]y=\log_2 2^{-3}[/tex]
[tex]y=-3[/tex]
Substitute [tex]x=\dfrac{1}{4}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{4}[/tex]
[tex]y=\log_2 \dfrac{1}{2^2}[/tex]
[tex]y=\log_2 2^{-2}[/tex]
[tex]y=-2[/tex]
Substitute [tex]x=\dfrac{1}{2}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{2}[/tex]
[tex]y=\log_2 2^{-1}[/tex]
[tex]y=-1[/tex]
Substitute [tex]x=1[/tex] in (i), we get
[tex]y=\log_2 1[/tex]
[tex]y=0[/tex]
Substitute [tex]x=2[/tex] in (i), we get
[tex]y=\log_2 2[/tex]
[tex]y=1[/tex]
The table of values is:
[tex]x[/tex] [tex]y[/tex]
[tex]\dfrac{1}{8}[/tex] [tex]-3[/tex]
[tex]\dfrac{1}{4}[/tex] [tex]-2[/tex]
[tex]\dfrac{1}{2}[/tex] [tex]-1[/tex]
[tex]1[/tex] [tex]0[/tex]
[tex]2[/tex] [tex]1[/tex]
Therefore, the first option is correct.
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Galileo improved the telescope and made important historic observations, including discovering four moons of _____. A. Mars B. Jupiter C. Saturn D. Neptune
Answer:
B: Jupiter
Step-by-step explanation:
hope this helps
Which measure is always the 50th percentile?
mean
median
upper quartile
Answer:
median
Step-by-step explanation:
the median is literally the middle number--half the numbers are higher, half the numbers are lower.
Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear
functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice's race?
Answer:Antonio had a head start of 3 meters
Step-by-step explanation:I took the test
Answer: Option B
(B) Antonio had a head start of 3 meters.
Step-by-step explanation:
In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of the part left? and also what is the area of the part left
Answer:
Perimeter = 98 cm
Area = 596 [tex]cm^{2}[/tex]
Step-by-step explanation:
Please refer to the attached image for the resultant figure when a quadrant of circle with radius 7 cm is cut from a rectangle of sides 30 cm and 25 cm.
Perimeter of a figure = Sum of all its sides + Perimeter of circle
Quadrant of a circle is one fourth of a circle and there are 4 such quadrant of a circle, so eventually there is one complete circle in this figure.
The sides of this resultant figure = 30 - 14 = 16 cm
and 25 - 14 = 11 cm
So perimeter of this figure = 16 + 11 + 16 + 11 + Perimeter of circle
[tex]\Rightarrow 54 + 2 \pi r\\\Rightarrow 54 + 2 \times \dfrac{22}{7} \times 7\\\Rightarrow 54 + 44 = 98 cm[/tex]
To find area of this figure = Area of rectangle - Area of circle
Area of rectangle = Length [tex]\times[/tex] Width
[tex]\Rightarrow 30 \times 25 = 750\ cm^{2}[/tex]
Area of circle = [tex]\pi r^{2}[/tex]
[tex]\Rightarrow \dfrac{22}{7} \times 7^{2} = 154\ cm^{2}[/tex]
So, area of figure = 750 - 154 = 596 [tex]cm^{2}[/tex]
Write the coefficients of x² in each of the following 1) 2+x²+x 2) 2-x²+x³
Answer:
(1) 1 (2) 0
Step-by-step explanation:
Looking at 1) 2+x²+x;
The coefficient of x is 1 because we see +x in the express which is the same as 1 × x = x.
2) Looking at 2) 2-x²+x³
There is no expression with x but we have x^2 , x^3 . Hence the coefficient of x is 0 because 0×x =0
Answer:
1) 1 and 2) -1
Step-by-step explanation:
1) 2+x²+x
+x² ⇒ coefficient of x² is 12) 2-x²+x³
-x² ⇒ coefficient of x² is -1A counterexample for sinytany=cosy is 0 degrees
true or false?
Answer:
False
sin (y) / cos (y) = cos (y)
cos (y) could be any value from -1 to 1.
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Write an explicit formula an, the nth term of the sequence 23,25,27
Answer:
2n+21
Step-by-step explanation:
rule = 2 so 2n
if n=1, 1x2=2 23-2=21
so +21
a 150 adults complete a survey 80 of them a woman what the ratio
Answer:
The number of men to number of women be 7 : 8 .
Step-by-step explanation:
Answer:
7:8
Step-by-step explanation:
a clock face has a circumference of 39.88 cm. What is the diameter of the clock ?
Answer:
diameter ≈12.7
Step-by-step explanation:
d= C/π so plug in what we know
39.88 ÷ 3.14 ≈ 12.7
Please look at photo and solve for y
Answer:
y = 45
Step-by-step explanation:
70 and y + 25 are corresponding angle and corresponding angles are equal when we have parallel lines cut by a transversal
70 = y+25
Subtract 25 from each side
70-25 = y
45 = y
[tex]answer \\ y = 45 °\\ solution \\ y + 25 = 70(being \: corresponding \: angles) \\ or \: y = 70 - 25 \\ y = 45 °\\ hope \: it \: helps[/tex]
One of the base for a trapezoid is 5in the other is unknown the height is 3in the area is 18in what is the other base.
Answer:
7 inches
Step-by-step explanation:
formula for a trepezoid is 1/2(a+b)*h
1/2(5+x)X3=18 (now make x the subject)
(5+x)X3=36
5+x=12
x=7
so the other base is 7in
Can someone please help me
Answer:
SSS
Step-by-step explanation:
3 sides are similar, so the triangles are similar.
Write as an algebraic expression
Answer:
18.) 10x
20.) k - 24
22.) 12 - 9
Step-by-step explanation:
Urgent! Please help fast! Estimate using mental math: 903.6 ÷ 29.1. Show how you would estimate mentally, then show your estimated answer.
Answer:
31
Step-by-step explanation:
I would use my fingers mostly.
But, I just do it normally. I pretend I'm using a sheet of paper then I write on it for the equation.
903.6 divided by 29.1
Then I estimate it because I know that 29.1 can go into 903.6 about 31 times. Then I multiply 31 and 29.1 and i get around 903.6.
I hope this helps. I'm sorry if you get this wrong.
Answer:
30
Step-by-step explanation:
Round 903.6 to 900 and 29.1 to 30
So 900/30
= 30
This would be my estimated answer
Also 30^2
= 900
HELP ME!!! Find the y intercept of the line y=2x-11
Answer:
It would intercept the y-axis at y = -11
Step-by-step explanation:
Here is the work
Answer:
Step-by-step explanation:
the y interception is -11
Y=mx+b formula the b is for the y intercept and the m is the slope.
Anyone mind helping out with my math?
Answer:
no
Step-by-step explanation:
all the numbers are multiples of each two.
For example,
2×2=4,
4×2=8,
8×2=16
So, the line would be linear.
// have a great day //
If karri takes a 7 question true false test and guess on every question, what is the probability that she gets all 7 questions correct? Answer in decimal form to 4 decimal places.
