Answer:
"35.84 years" is the appropriate solution.
Step-by-step explanation:
The given values are:
Rate of savings generation,
[tex]s'(t)=300e^{\frac{t}{20} }[/tex]
System cost to install,
= $30000
Now,
The total savings will be:
⇒ [tex]s(t)=\int\limits s'(t) \ dt[/tex]
On substituting the values, we get
⇒ [tex]= \int\limits 300e^{\frac{t}{20} } \ dt[/tex]
⇒ [tex]s(t)=\frac{300e^{\frac{t}{20} }}{\frac{1}{20} }+c[/tex]
When,
Savings = 0
t = 0, then
⇒ [tex]0=6000e^o+c[/tex]
⇒ [tex]c=-6000[/tex]
The formula will be:
⇒ [tex]s(t)=6000[e^{\frac{t}{20} }-1][/tex]
On putting the values in the above formula, we get
⇒ [tex]30000=6000(e^{\frac{t}{20} }-1)[/tex]
[tex]5=e^{\frac{t}{20}}-1[/tex]
[tex]e^{\frac{t}{20} }=6[/tex]
On taking log, we get
⇒ [tex]\frac{t}{20} =log \ 6[/tex]
[tex]t=20 log 6[/tex]
[tex]=35.84 \ years[/tex]
PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!
Answer:
They have air-filled pockets in their leaves
Step-by-step explanation:
Factor 8b^3 – 4b^2 a - 18b + 9a completely.
Answer:
85
Step-by-step explanation:
Answer:
(2b-a)x(2b-3)x(2b+3)
Step-by-step explanation:
4x^2+2x-1=0 in quaratic equations
Answer:
Step-by-step explanation:
"quaratic" should be "quadratic."
The coefficients of this quadratic are 4, 2 and -1. Thus, the discriminant is
b^2 - 4ac, or here, 4 - 4(4)(-1) = 20
Since the discriminant is positive, our quadratic has two real, different roots.
-2 ± (√4)(√5)
The roots are: x = ---------------------
2(4)
-1 ± √5
This reduces to x = ---------------
8
Please answer <33 I would lava it :)
Answer:
5 gallons
Step-by-step explanation:
3/4 + 6/8 + 20/8 + 1
6/8 + 6/8 + 20/8 + 8/8
40/8 = 5 gallons
How can the next term in the infinite sequence 1, 5, 12, 22, 35, ... be generated?
A. Square the term number, subtract the tem number from the result, multiply by 3, and divide the result by 2.
B. Square the term number, multiply the result by 3. divide by 2, and subtract the term number from the result.
C. Square the term number, divide the result by 2 subtract the term number, and multiply the result by 3.
D. Square the term number, multiply the result by 3 subtract the tem number, and divide the result by 2.
Answer:
Its D
Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2
Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:
What is the distance, CD, between the boats?
230.9 ft
284.3 ft
115.5 ft
173.2 ft
Answer:
Option (1)
Step-by-step explanation:
By applying tangent rule in ΔABD,
tan(30°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AB}{BD}[/tex]
BD = [tex]\frac{AD}{\text{tan}(30)}[/tex]
BD = [tex]\frac{200}{\frac{1}{\sqrt{3} } }[/tex]
BD = 200√3 ft
By applying tangent rule in ΔABC,
tan(60°) = [tex]\frac{AB}{BC}[/tex]
[tex]\sqrt{3}=\frac{200}{BC}[/tex]
BC = [tex]\frac{200}{\sqrt{3}}[/tex]
Since, CD = BD - BC
CD = 200√3 - [tex]\frac{200}{\sqrt{3}}[/tex]
= 346.41 - 115.47
= 230.94 ft
≈ 230.9 ft
Therefore, Option (1) will be the correct option.
Answer:
230.9 ft
Step-by-step explanation:
person above said it was correct answer
use multiples to determine the LCM of 45and 60
Answer:
LCM of 45 and 60: 180
Step-by-step explanation:
Graph y=−2x+5 and y=−12x−3 . Are the lines parallel, perpendicular, or neither?
$12 with a 85% markup
12+85% is $22.20
80%x12=9.6
5%x12=0.6
9.6+0.6=10.2
12+10.2=22.20
Answer: $22.20
Solve the system by substitution: 3x - y = 21 and y = 6x
No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files. No files.
Answer:
if y=6x then 3x-6x=21
-3x=21
x=-7
3x - y = 21
y = 6x
We see that,
0 = 42 which is not true.
The system of equations has no solutions.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
System of equations:
Conditions:
1 - If we get x = n (a value)
The system of equations has one solution
2 - If we get x = x or y = y or n = n
The system of equations has infinite solutions.
3 - If we get n ≠ 0
The system of equations has no solutions
Now,
3x - y = 21 _____(1)
y = 6x ______(2)
From (1) we get,
3x = 21 + y
x = (21 + y) / 3 _____(3)
Putting (3) in (2) we get,
y = 6 [(21 + y) / 3]
y = 2 (21 + y)
y = 42 + y
0 = 42
Which is not true.
This means the system of equations has no solutions.
Thus,
The system of equations has no solutions.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Find (a) the range and (b) the standard deviation of the data set 40,35.45,55,60. Round to the nearest hundredth if necessary.
Answer:
(a) 25
(b) 9.27
Step-by-step explanation:
Step 1
We have to rearrange the given days set from least to highest
35, 40, 45, 55, 60
(a) the range
Range = The highest number - The least number
= 60 - 35
= 25
(b) the standard deviation of the data set
35, 40, 45, 55, 60.
We find the Mean
Mean = Sum of values/Number of values
= 35+40+45+55+60/5
= 235/5
= 47
We can find the standard deviation now.
The formula =
√(x - Mean)²/n
= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5
= √144 + 49 + 4 + 64 +169/5
= √430/5
= √86
= 9.273618495
Approximately = 9.27
Answer this question to get marked as barinliest!!!!
can someone please answer these
*will give brainliest if you answer all* AND NO LINK
Answer:
Rectangular Prism → h = 2in
B = 143in
P = 48in
Surface Area = 382in²
Lateral Surface Area = 96in²
Triangular Prism → h = 7in
B = 20in
P = 27in
Surface Area = 229in²
Lateral Surface Area = 189in²
Triangular Prism → h = 10in
B = 120in
P = 60in
Surface Area = 840in²
Lateral Surface Area = 600in²
Step-by-step explanation:
Formulas: Total Surface Area = 2B = Ph
a²+b²=c²
Area = [tex]\frac{1}{2}[/tex]bh
Lateral Area = Ph
PLUG NUMBERS INTO FORMULA. (I'm too lazy to type it all out lol)
Suppose there are 8 boys and 7 girls in a classroom. If one student is chosen at random to run a errand. What is the probability that the student will be a girl?
Answer:
7/15
Step-by-step explanation:
7+8=15
there's 7 girls so you have 7/15 chance of getting a girl
Answer:
8/15
Step-by-step explanation:
possibilities/sample size= 8 girls/ 15 students
Find the area of this figure
Answer:
45cm
Step-by-step explanation:
3 x 5 x 3 x 1/2
(if im wrong im sorry)
You are given two pairs of triangles. For the first pair of triangles, each side and angle of one triangle is congruent to the corresponding side and angle of the other. You show that rigid motions can transform one triangle so that it matches up with the other. For the second pair of triangles, you show that rigid motions can transform one triangle so that each angle or side of one triangle matches exactly with a corresponding angle or side of the other triangle. What have you proved?
Options:
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.
b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Step-by-step explanation:
For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.
When rigid transformation is applied to a shape, the image (i.e. result) of the transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.
Option (c) is true
which of the following expressions are equivalent to -2/3? select all that apply
A. -1/9 x 6
B. -15 ÷ 10
C. 12 ÷ -18
D. -3/4 ÷ 1/2
E. -8/9 x 3/4
Answer:
A.
C.
E.
Step-by-step explanation:
A
-1/9×6=
-1/9×6/1= -6/9 = -2/3
B
-15 ÷ 10
-15/1 ÷ 10/1
-15/1 × 1/10 = -15/10 = -3/2
C
12 ÷ -18 =
12/1 ÷ -18/1 =
12/1 × -1/18 = -12/18 = -2/3
D
-3/4 ÷ 1/2 =
-3/4 × 2/1 = -6/4 = -3/2
E
-8/9 × 3/4 = -24/36 = -2/3
find the surface area to the nearest tenth
Step-by-step explanation:
Surface Area of Figure = Area of 4 triangular sides + Area of Base
=
[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]
What is the measure of the other acute angle? Pls explain how you got your answer
Answer:
30 degrees
all triangles equal 180 degrees
90+60=150
180-150=30
Step-by-step explanation:
Which situation CANNOT be represented by this equation? 6−7=29 6 x - 7 = 29 CLEAR CHECK Joel earns $7 $ 7 per hour to mow his aunt's lawn. If he spends $6 $ 6 on gas, how many hours, x , will he need to mow to have $29 $ 29 left? Joel mows his aunt's lawn for $6 $ 6 per hour. If he spends $7 $ 7 on gas, how many hours, x , will he need to spend mowing the lawn to have $29 $ 29 left? Joel takes 6 6 hours to mow his aunt's lawn. If he spends $7 $ 7 on gas, how much does he get paid per hour, x , to mow the lawn and still have $29 $ 29 left?
Answer:
Joel earns $7 per hour to mow his aunt's lawn. If he spends $6 on gas, how many hours, x , will he need to mow to have $ 29 left?
Step-by-step explanation:
The given equation is :
6x - 7 = 29
It is given that total hours be = x
Joel earns $7 per hour, so the total earning of Joel in x hours is = $ 7x
He spends $6 on gas, so = 7x - 6
He is left with $ 29 after spending on gas.
Therefore, the equation becomes :
7x - 6 = 29
Clearly, it can be seen that in this case, the given situation cannot be represented by the given equation, i.e. 6x - 7 = 29.
PLSS HELP MEE AND NO BOTS I WILL REPORT Find the equation of the line below. If necessary, use a slash (/) to indicate a
division bar.
(6,1)
Can someone plz help me with these United rates and explain step by step ?
Which can be used to find the partial sum of the
first six terms?
1-55
4
1-59
1-5
1-5
(
이는
O O
(1-5)
1-5
1-65
1-6
4
DONE
Answer: A
Step-by-step explanation: Edge 2020
Answer:
A
Step-by-step explanation:
Correct on EDGE 2022
picture is shown !
Complete the remainder of the
table for the given function rule:
y = -2x + 9
please help
Answer: 17; 13; 9; 5; 1
Step-by-step explanation:
y = -2x + 9
When x = -4, y = 17
When x = -2 , y = -2x + 9 = -2(-2) + 9 = 13
When x = 0 , y = -2x + 9 = -2(0) + 9 = 9
When x = 2 , y = -2x + 9 = -2(2) + 9 = 5
When x = 4 , y = -2x + 9 = -2(4) + 9 = 1
A trapezoid has angles 54 degrees, 54 degrees, x, and x. Look at the trapezoid shown. What is the measure of angle x? The measure of each angle x is 54° 90° 126° 252°
Answer: the answer is C 126°
Answer pleaseeee!!!!!!!!!!!!!!!!
Answer:
[tex] m \angle \: 3 = 94 \degree[/tex]
Step-by-step explanation:
[tex]m \angle \: 3 + 86 \degree = 180 \degree \\(linear \: pair \: \angle s) \\ \\ m \angle \: 3 = 180 \degree - 86 \degree \\ \\ m \angle \: 3 = 94 \degree \\ \\ [/tex]
1)
The fourth-grade students are taking a field trip and need to rent minivans. Each minivan will hold 8 people. There are 135 people
going on the trip. How many people will not be able to go if they only rent 16 minivans?
A) 6 people
B) 7 people
C)8 people
D) 9 people
PLEASEE HELP
ILL GIVE BRAINLIEST
Answer:
d. 9
Step-by-step explanation:
i friken used all my attempts guessing on this and got it wrong all times so 9 is the last answer
Plz help! Due tonight!
During halftime of a football game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 80 feet per second. The T-shirt is caught 41 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Can someone plz help me
Answer:
IT's d!!!!!
Step-by-step explanation:
Two parallel lines, I and m, are cut by a transversal, t, as shown below.
1
(17x + 14)
((48-2°
m
What is the value of z?
Answer:
x = 8
Step-by-step explanation:
alternate-interior angles equal 180°
17x + 14 + 4x - 2 = 180
21x + 12 = 180
21x = 168
x = 8