Answer:
21.96 ; 24.72
Step-by-step explanation:
Given that :
Give the equation:
A(t) = 700(1.03)^t
A.)
Average rate of change over the first 4 years ;
(t=0 to t=4)
At t = 0
A(0) = 700(1.03)^0 = 700
A(1) = 700(1.03)^1 = 721
A(2) = 700(1.03)^2 = 742.63
A(3) = 700(1.03)^3 = 764. 9089
A(4) = 700(1.03)^4 = 787.856167
[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4
= 87.856167 / 4
= 21.96404175
= 21.96
Over the 2nd 4 years :
A(4) = 700(1.03)^4 = 787.856167
A(5) = 700(1.03)^5 = 811.49185201
A(6) = 700(1.03)^6 = 835.8366075703
A(7) = 700(1.03)^7 = 860.911705797409
A(8) = 700(1.03)^8 = 886.73905697133127
[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4
= 98.88288997133127 / 4
= 24.72
A given field mouse population satisfies the differential equation dp/dt=.4p-450 where p is the number of mice and t is the time in months.
(a) Find the time at which the population becomes extinct if p(0)=1075
Round your answer to two decimal places in months.
(b) Find the initial population Po if the population is to become extinct in 1 year.
Round your answer to the nearest integer.
Po= mice
Answer:
a) 7.78 months
b) 1116
Step-by-step explanation:
Given -
[tex]\frac{dP}{dt} = 0.4p-450[/tex]
Integrating the above equation with respect to time, we get -
[tex]\int\ \frac{dP}{0.4p-450} = \int\ dt\\[/tex]
let us define new variable x
[tex]x = 0.4p - 450 \\dx = 0.4 dy[/tex]
substituting these values in above integral equation, we get -
[tex]\frac{1}{0.4} \int\ \frac{dx}{x} = \int\ dt\\ln x = 0.4 t + C\\x = ce^{0.4t}[/tex]
[tex]P (t) = \frac{C}{0.4} e^{0.4t} +1125\\[/tex]
at t = 0, P (0) = 1075, using this condition, we get -
[tex]\frac{c}{0.4} = -50\\P(t) = 50 e^{0.4t} +1125 \\t = 7.78\\P(0) = 1125 - \frac{1125}{e^{4.8}} = 1116[/tex]
Write the equation of the line that passes through the points (-3, 4) and (-3,3).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
x=-3
Step-by-step explanation:
y-4=(3-4)/(-3-(-3))(x+3)
y-4=1/(-3+3) (x+3)
y-4=1/0(x+3)
or x+3=0
x=-3
Can someone help me, please??
Answer:
im gonna say its the last one
Step-by-step explanation:
all of the graphs and histograms ive seen have a 0 at the y
Is this theorem AA, SSS, or SAS? If so how do you know?
If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
Answer:
it’s A. (f+g)(x) is greater than or equal to 3 for all values of x.
Step-by-step explanation:
I got it right on the test.
Answer:Yoo the anser is A
Step-by-step explanation:
for the makeupo math corse
-(f + g)(x) 3 for all values of x
You take your favorite teacher out to lunch. The total
cost of your meals was $37.50. You want to add a 20%
tip. What is the new final total?
Answer:
it would be 45 total with the 20%
Can some write the correct inequality graph below
Answer:
x≥-6
Step-by-step explanation:
Mhanifa please help I will mark brainliest
Answer:
36°90°Step-by-step explanation:
Question 1
x = 180° - 2*72° = 180° - 144° = 36°Question 2
x + 2(x/2) = 180°2x = 180°x = 90°karl can flip 3 water bottles in 1/8 of a minute at that rate how many bottles can we expect him to flip in 1 minute
Answer:
Step-by-step explanation:
x/1=3/(1/8)
x=3(8/1)=24 bottles per minute
The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y=8.42x+800, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 145 minutes.
Answer:
685ik
Step-by-step explanation:
uuuuuuyyyyyyyyyyyyyyyyty
plus the wat
5.6t
Determine whether the ratios are equivalent 6 : 10 and 12 : 20 ?
Answer:
Yes, they are equivalent because 12 is divisible by 6 two times and 20 is divisible by ten two times.
A popular sports drink uses sugar as a sweetener. The radio of pints of spors drink to grams of sugar is 5:16.
Erika only wants to consume 4 grams of sugar from her sports drink.
How many pints of the sports drink can erika drink?
Answer:
¯\_(ツ)_/¯
Step-by-step explanation:
The equation Y+B=3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?
Oy-x-3
O y-3x+9
O y-sx-9
O y-3x+3
Answer:
[tex]y = 3x - 27-b[/tex]
Step-by-step explanation:
Given
[tex]y + b = 3(x - 9)[/tex]
Required
Write in slope intercept
Open bracket
[tex]y + b = 3x - 27[/tex]
Collect Like Terms
[tex]y = 3x - 27-b[/tex]
PLEASE HELP! PLEASE ALSO GIVE A GOOD EXPLANATION AND SHOW WORK! 45 points!!
Dalia is painting her room. After painting 1/10 of her room, Dalia has used 1/2 of a can of paint.
Select ALL of the true statements.
1. Painting 1/2 of Dalia's room requires 10 cans of paint.
2. Each can of paint will cover 1/20 of Dalia's room.
3. 3 cans of paint will cover 60% of Dalia's room.
4. Dalia's entire room requires 20 cans of paint.
5. Dalia's entire room requires 5 cans of paint.
Hence statement 3 and 5 are true from the equation given in question.
What is equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Types of Equations:
Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1.
Quadratic Equation: This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2.
Cubic Equation: A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3.
Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.
Number of cans used 1/10 part of room = 1/2
No. of cans paints used 1 part = 1/2 / 1/10 = 5
∵ 1/2 can paint is used = 1/10
∴ 1 can paint used = (1/10)*2 = 1/5
∴ 5 cans = 100%
3 cans used = (3/5)*100 = 60%
To know more about equation please visit:
brainly.com/question/10413253
#SPJ2
Find the product (6x² + 2x)(x²+4x)
Answer:
6x⁴ + 26x³ + 8x²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Step-by-step explanation:
Step 1: Define
(6x² + 2x)(x² + 4x)
Step 2: Expand
FOIL: 6x⁴ + 24x³ + 2x³ + 8x²Combine like terms: 6x⁴ + 26x³ + 8x²A manager uses the following equation to predict monthly receipts: Y-450-10 Lt time in weeks and y = receipts.) What is the forecast for July 14th ift=4 is the fourth week in January and t = 6 is February 14th of the same year (assume there are 4 weeks in each month)?
a. 690
b. 710
c. 730
d. 750
A major reason that decision making is often not such a rational process is that there are: Suppose we have H0:µ1= µ2 versus HA: µ1 ≠ µ2, with level of significance of α =.05 and critical values of zα/2 = ± 1.96, and the computed Test Statistics value of Z = -1.07. What is our decision?
Answer:
b. 710
Fail to reject H0
Step-by-step explanation:
Forecast for July 14 :
Assume there are 4 wwwks in each month :
January to June = ( 4 * 6 months) = 24 weeks in 6 months ;
July - July 14 = 2 weeks :
2 + 24 = 26 weeks
The model given :
Y = 450 + 10t
Y = 450 + 10(26)
Y = 450 + 260
Y = 710
2.)
Test is a 2 tail test :
Zstatistic = - 1.07
At 95% confidence = ±1.96
Zcritical = - 1.96
Hence,
Reject H0 if ;
Zstatistic < Zcritical
-1.07 > 1.96
Hence, fail to reject H0.
5(3x - 7 + 4y)
*
+
Your answer
Answer:
15x - 35 + 20y
Step-by-step explanation:
distribute
5 x 3x = 15x
5 x -7 = -35
5 x 4y = 20y
Find the x and y intercepts of this line:
-5x+4y=-18
Answer:
Step-by-step explanation:
x- intercepts: ( 18/5,0)
y- intercepts: ( 0,-9/2)
un numero entero y racional
Answer:
Los números racionales son aquellos números que pueden ser expresados como una relación entre dos enteros. Por ejemplo, las fracciones 1/3 y –1111/8 ambas son números racionales. Todos los enteros están incluídos en los números racionales, ya que cualquier entero z puede ser escrito como la relación z /1.
Step-by-step explanation:
A triangle with side lengths of 15, 18, and 25 is a right triangle. True or False
What is the slope of the equation y- 5 = -3x?
Answer:
-3/1
Step-by-step explanation:
It's always the x value over the y value, so whatever's in the x
Answer:
-3
Step-by-step explanation:
the equation is y=-3x+5, so m=-3
What two numbers multiply to get -30 and add to get -7 ?
Answer:
3 and -10 to get 30
4 and -11 to get -7
Step-by-step explanation:
3 * -10 = -30
4 + (-11) = 4 - 11 = -7
The marked price of a sweater at the clothing store was $24.
During a sale, a discount of 25% was given. A further 15%
discount was given to the customers who have the store's
credit card. How much would a member customer need to pay
for the sweater during the sale if the customer paid with the
store's credit card? Round your answer to the nearest cent.
Answer:
Ambitious Ambitious Ambitious Ambitious
Help me please!...ffddfdf
Answer:
Radius:3.5 or 7/2
Diameter:7
Step-by-step explanation:
The diameter is given, and the radius is half of the diameter because it's from the middle of the circle to the edge. Divide 7 by two and you get radius
Please help ASAP will give Brainlyest answer :M/5=2
A $230 suit is marked down by 30%. Find the sale price.
Answer:
161
Step-by-step explanation:
69 is 30% of 230 so 230-69=161 is the answer.
Helppppp pleaseeee thanks ✏️
Answer:
H
Step-by-step explanation:
Sum of angles in a triangle is 180 degrees
That means
180= 25 + 45+ unknown angle
180= 70 + unknown angle
180 - 70 = unknown angle
110 = unknown angle
Help plz I will give you BRAINLYST I don't know if I spelled that right lol but plz and I will give you a follow!?!?!?!?
The value of 34 + 5 ⋅ 5 = ___.
Answer:
59
34+5×5=34+25=59
Does anyone know the answer and could you explain how you got your answer? THANK YOUU
Answer:
This would be a 60% increase
Step-by-step explanation:
40-25 and divided by 25 times 100
you should get 15/25 multiply it by 100=60%
NEED HELP ASAP!!! for geometry class
Answer:
B) AAS
Step-by-step explanation:
B) AAS