Answer:
a) 2%
b) 0.17%
Step-by-step explanation:
Exponential growth is modeled by the equation ...
y = a·b^x
where 'a' is the initial value, and 'b' is the growth factor.
When x is has units of time, the growth factor 'b' applies over 1 unit of x. The applicable growth factor for different units of time can be found using the rules of exponents applied to the equation written with x expressed in the different units.
The growth rate is related to the growth factor by ...
b = 1 +r . . . . where r is the growth rate
r = b -1 . . . . solved for r
__
a)Your equation is ...
V = 300(1.02^t)
where t is expressed in years. Then the corresponding annual growth rate is ...
b = 1.02
r = b -1
r = 1.02 -1 = 0.02 = 2% . . . annual rate of growth
__
b)When the equation is written so that t is expressed in months, it becomes ...
V = 300(1.02)^(t/12)
V = 300(1.02^(1/12))^t
Now, the growth factor (per month) is
b = 1.02^(1/12)
and the monthly growth rate is ...
r = 1.02^(1/12) -1 ≈ 1.00165158 -1 = 0.00165158
r ≈ 0.17% . . . . monthly rate of growth
4 x 5-10 - 2 (1-2) + 5=
Answer:
[tex]17[/tex]
Step-by-step explanation:
[tex]4\cdot \:5-10-2\left(1-2\right)+5[/tex]
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]=4\cdot \:5-10-2\left(-1\right)+5[/tex]
[tex]=20-10-2\left(-1\right)+5[/tex]
[tex]=20-10-\left(-2\right)+5[/tex]
[tex]20-10=10[/tex]
[tex]=10-\left(-2\right)+5[/tex]
[tex]-\left(-2\right)=+2[/tex]
[tex]=10+2+5[/tex]
[tex]10+2=12[/tex]
[tex]=12+5[/tex]
[tex]12+5=17[/tex]
[tex]=17[/tex]
a cone has a volume of 150.72 cubic millimeters and a height of 9 millimeters what is the radius
The volume of a cone is the amount of space in the cone
The radius of the cone is 4.00 millimeters
How to determine the radiusThe given parameters are:
Volume = 150.72 cubic mL
Height = 9 mL
The volume of a cone is calculated as:
[tex]V = \frac 13 \pi r^2h[/tex]
So, we have:
[tex]150.72 = \frac 13 \pi * r^2 * 9[/tex]
Divide
[tex]150.72 = \pi * r^2 * 3[/tex]
Divide both sides by 3
[tex]50.24 = \pi * r^2[/tex]
Rewrite the equation
[tex]50.24 = \frac{22}{7} * r^2[/tex]
Solve for r^2
[tex]r^2 = 50.24 * \frac{7}{22}[/tex]
Solve for r
[tex]r = 4.00[/tex]
Hence, the radius of the cone is 4.00 millimeters
Read more about volume at:
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what is the surface area of the Triangular prism? Pls answer ASAP I WILL GIVE BRAINLIEAST.
Answer:
170cm²
Step-by-step explanation:
so the middle rectangle part first
15x10=150
then there's triangles so i'm gonna skip the divided by 2 part.
5x4=20
150+20=170
Solution:
Note that:
Surface area = 2(Area of triangle) + 3(Area of rectangle)Finding the area of triangle:
Area of triangle = 1/2 x 4 x 5=> Area of triangle = 1/2 x 20Area of triangle = 10 cm²Finding the area of rectangle:
Area of rectangle = 5 x 10=> Area of rectangle = 50 cm²Using the formula of surface area:
Surface area = 2(Area of triangle) + 3(Area of rectangle)=> Surface area = 2(10) + 3(50)=> Surface area = 20 + 150=> Surface area = 170 cm²What is 3(2x -5) + 10 ≥ 25?
An explanation would be thanked and also given brainlyist (づ￣ 3￣)づ
Answer:
x>_5
Step-by-step explanation:
distribute ---> 6x-15+10_>_25... add 5 to both sides 6x_>_ 30... then divide by 6... x>_5
Last week, a chocolate shop sold 5 ounces of white chocolate. It sold 1 9/10 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
Write your answer as a fraction or as a whole or mixed number.
Answer:
9.5
Step-by-step explanation:
What is the value of X
I'll give brainliest to the first one correct
Answer:
x=28.3
Step-by-step explanation:
Figure A is a scale image of Figure B
Answer:
x = 30
Step-by-step explanation:
Put in proportions [tex]\frac{x}{45}[/tex] = [tex]\frac{18}{27}[/tex]
Cross multiply and get 27x = 45 x 18
OR...
27x = 810.
THEN...
divide by 27 on both sides to get 30
x = 30
Rehman invests his summer earnings of
$3050. He invests part of the money at
8%/year, and the rest at 7.5%/year. After
1 year, these investments earn $242 in
simple interest. How much did he invest
at each rate?
Answer:
Step-by-step explanation:
let Rehman invests in 8%=$x
simple interest=x*0.08*1=0.08 x
investment in 7.5%=$(3050-x)
simple interest=(3050-x)*0.075*1=228.75-0.075x
total interest=0.080 x+228.75-0.075 x=0.005x+228,75
0.005x+228.75=242
0.005 x=242-228.75
0.005 x=13.25
x=13.25 /0.005=2650
invested at 8%=$2650
invested at 7.5 %=3050-2650=400
Simplify the following
1.) 5xy - xy + 2x - 13x + 10xy - 8x
2.) -6c - (-6c) - (+6c)
3.) 0x -22x - 4(2x)
yea someone just help me again.
Hakeem puts $53 from each paycheck into his savings account. He gets paid every two weeks or 26 times per year. His goal is to save $1,300 this year
Step-by-step explanation:
53×26=1378. hence if hakeem saves $1300 he still has about $78.
Find the area of the trapezoid using the formula using the A=1/2h(b1+b2)
Answer:
9
Step-by-step explanation:
1/2 bh (b1+b2)Count all the squares for the base (6 squares)Half it bc 1/2bh, which is not 3(h)Now count the amount of squares to the top of it from the bottom (3 as well)Now the problem is 3(3) which is 9.So, the answer is 9Hope this helps! Comment on it if you need more explanation!:)
Answer: 9
Step-by-step explanation: beacuse it is
Consider a tire with a radius of 9 inches that is rolled 150 revolutions and travels
approximately 8,482 inches.
The tire with radius of 6 inches when rolled 150 revolutions travels approximately 5654 inches.
Equation
An equation is an expression that shows the relationship between two or more numbers and variables.
A tire with a radius of 9 inches that is rolled 150 revolutions and travels approximately 8,482 inches.
For a tire with radius r and that is rolled 150 revolutions and travels approximately 5654 inches:
9/8482 = r/5654
r = 6 inches
The tire with radius of 6 inches when rolled 150 revolutions travels approximately 5654 inches.
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what is 1*727/3+6*2-5=? pIz help!!!
Answer:
its 249 1/3
Step-by-step explanation:
=727/3 + 6 x 2 - 5
=727/3 + 12 - 5
= 748/3
= 249 1/3
what is the value of x?
Answer:
45??
Step-by-step explanation:
Answer:
x = 15√2
Step-by-step explanation:
Since the two angles on the triangle are the same, we can conclude that x is equal to the side that is adjacent to it too ( not the hypotenuse).
We will have x = a to use this pythagorean theorem as follows.
We will get the equation,
a = b
where
a^2 + b^2 = c^2
so,
a^2 + a^2 = c^2
2a^2 = 30^2
2a^2 / 2 = 900 / 2
√a^2 = √450
a = √450
a = 15√2
Your welcome, comment below if you have any questions! If you could mark this as brainliest I would appreciate it :D
p: x is an even number. If x = 3, then ~p is true or false
helpppp
Answer:
False
Step-by-step explanation:
2,4,6,8,10,12, ETC
I need help please! I will mark you as a brainlest and give out 30 points!
The sum of two numbers is 75. Their difference is 25. What are the two numbers?
Show all work
Answer:
50 and 25
Step-by-step explanation:
y+x=75
y-x=25
y+y=yx and x-x eliminate itself
so now we have the operation 2y= 50, I got the 50 from substrating 25 from 75
now found the value of y, 50/2=25
so y=25
now plug the number in
25+x=75
75-25=50
so x= 50
Jen can jump rope 80 times in 60 seconds. If she jumps at a constant ratio of seconds to jumps, how many jumps can she make in 15 seconds?
Answer:
5 jumps per 15 seconds
Step-by-step explanation:
60/15 = 4
80/15 = 5
Have an amazing day!
Please mark brainliest!
Max has two cats. Rex and Roman. If Rex weighs 11 7/18 pounds and Roman weighs 11.329 pounds, which cat weighs the most?
Answer: Rex weighs more.
Step-by-step explanation:
You have to change both of the numbers into the same form. I did decimal form.
Rex - 11 7/18 = 11.389 (rounded to the hundredths)
Roman - 11.329
Rex is bigger.
Hope this helps!
H(n)=n+2
g(n) = 2n + 1
Find h(n) − g(n)
Answer:
-n + 1
Step-by-step explanation:
(n + 2) - (2n + 1)
n + 2 - 2n - 1
-n + 1
Answer:
[tex] \sf \: -n + 1 [/tex]
Step-by-step explanation:
Given information,
→ h(n) = n + 2
→ g(n) = 2n + 1
Now we have to,
→ find the value of h(n) - g(n).
Then required value will be,
→ h(n) - g(n)
→ (n + 2) - (2n + 1)
→ n + 2 - 2n - 1
→ (n - 2n) + (2 - 1)
→ (-n) + (1)
→ -n + 1
Hence, the value is -n + 1.
I REALLY NEED UR HELP PLEASE!
I need help with 4 and 5
Answer:
4) It does not represent a function because multiple outputs are equal to an input.
(i dont know for b sorry)
5) i think that means ummm:
(-6, -12)
(-3, 6)
(0, 0)
(3, -6)
(6, -12)
Step-by-step explanation:
because thats what i think. i tried my best here hope this helps!
If f(–5) = 0, what are all the factors of the function f (x ) = x cubed minus 19 x 30? Use the Remainder Theorem. (x – 2)(x 5)(x – 3) (x 2)(x – 5)(x 3) (x – 2)(x 5) (x 2)(x – 5).
Answer:
A. (x – 2)(x + 5)(x – 3) on edg
Step-by-step explanation:
Took the test
When a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial. The factors of x³-5x+6 are (x+5)(x-2)(x-3).
What is the Remainder theorem?According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
Since f(–5) = 0, therefore, (x+5) is a factor of the polynomial f(x).
[tex]\dfrac{x^3-19x+30}{x+5} = x^2-5x+6[/tex]
Now, x² -5x + 6 can be factorised as,
x² - 5x + 6
x² - 2x - 3x + 6
x(x-2) -3 (x-2)
(x-2)(x-3)
Hence, the factors of x³-5x+6 are (x+5)(x-2)(x-3).
Learn more about the Remainder Theorem:
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What type of number is 0.55/0.55
Answer:
Whole number
Step-by-step explanation:
Whole number because it equals one and one is a whole number.
Is it impossible for a triangle to be both right and acute
The 225 students who passed all of their classes on the last report card will attend a one-hour Friday Fun-Day sponsored by the Parent-Teacher
Organization (PTO). A variety of activities and snacks will be provided and students will receive one prize. A random survey of 50 students was
conducted to determine how many of each prize should be purchased for the Friday Fun-Day. The results of the survey are shown.
• 28 students want a slime kit.
• 12 students want a basketball.
• 6 students want a jewelry bead kit.
• 4 students want an artist sketch pad and pencil set.
Problem
Based on the survey results, which of these is NOT a valid prediction of the prizes wanted by the 225 students?
A There are 126 students who want a slime kit.
B There are 36 fewer students that want an artist sketch pad and pencil set than a basketball.
C There are 71 students who want either a basketball or a jewelry bead kit.
D There are 27 more students who want a slime kit than all the other prizes combined.
Answer:
C. is incorrect.
Step-by-step explanation:
Calculate the percentages for each prize desired by the 50 students responding in the sample survey. See the attached image for this calculation. Multiply these percentages times the total student body of 225 students to determine the likely selection for each prize (on the attachment).
A. is correct (126 students)
B. is correct
C. is incorrect. The total is (54 + 27) = 83
D. is true
If the total surface area of a cube is 96cm², find its volume
======================================================
Explanation:
Let's find the side length of the cube based on the given surface area.
SA = 6s^2
96 = 6s^2
6s^2 = 96
s^2 = 96/6
s^2 = 16
s = sqrt(16)
s = 4
The cube has side length 4 cm.
Now calculate the total volume.
V = s^3
V = 4^3
V = 4*4*4
V = 64 cubic cm.
-------------------
Extra info:
The unit "cubic cm" can be abbreviated to "cc". So whenever you hear something from a medical tv show "get me 10 cc's of XYZ", that's what they're referring to. Of course the "10" might be some other realistic value, it's just an example.
1 cc = 1 milliliter
1. Two containers are being filled with water. One begins with 10 gallons of water and is filled at a rate of 2.5 gallons per minute. The other begins with 24 gallons and is filed at 2.25 gallons per
minute.
Part A: Write an equation that represents the amount of water w, in gallons, with respect to time t, in minutes, for each container
Part B: Solve the system of equations. Show your work
Part C: How long would it take for both of the containers to have the same amount of water? How much water would be in each container?
Answer: PART A:
w-3.5 t=8
w-3.25t=24
PART B:
t=64
and w= 232
PART C:
It will take 64 minutes for both of the containers to have the same amount of water.
The amount of water in each container is:
232 gallons.
Step-by-step explanation:
PART A:
Let the water is filling in 't' minutes.
and 'w' denotes the amount of water in the container.
for container 1:
One begins with 8 gallons of water and is filled at a rate of 3.5 gallons per minute.
The equation is given by:
or
for container 2:
The other begins with 24 gallons and is filled at 3.25 gallons per minute.
The equation is given by:
or
PART B:
on solving equation (1) and equation (2) by method of elimination we get:
subtract equation (2) by equation (1) to obtain:
t=64
and putting the value of t in equation (1) to obtain:
w= 232
PART C:
Hence it will take 64 minutes for both of the containers to have the same amount of water.
The amount of water in each container is:
232 gallons.
Step-by-step explanation:
What is the perimeter of the basement floor? _____ feet
Answer:
106
Step-by-step explanation:
You just have to add all the sides together.
9+31+22+13+18+(31-18)
=106
A pail contains a certain amount of water. After Peter used it to fill a 1.5 liter can, a 750 milliliter bottle, and a 2 liter 250 milliliter tin, he realized that he had a liter of water left in a pail. How much water was in the pail at first? explain and show your work.
Answer:
After Peter used it to fill a 1.5 liter can, a 750 milliliter bottle, and a 2 liter 250 milliliter tin, he realized that he had a liter of water ...
Step-by-step explanation:
