The function that represents the amount of money in the account after t years is f(t) = $2000(1.0033^12t).
The money in his account in five years would be $2442.
The number of years it would take to have a value over $2500 is 6 years.
What is the future value of the account?The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsf(t) = $2000(1.0033^60) = $2442
f(6) = $2000(1.0033^72) = 2535.41
To learn more about future value, please check: https://brainly.com/question/18760477
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answer:
76 squared cm
Step-by-step explanation
the equation is (b+b*h/2) so u just take 7 plus 12 times 8 divided by 2 and you get 76
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answer:
30yd²
Step-by-step explanation:
A = a*b/2 = 5yd * 12 yd / 2 = 60 yd² / 2 = 30 yd²
Answer: 30 yd²
Step-by-step explanation:
Let's start by flipping the triangle over to become a standard right-angled triangle so that the side measuring 5 yards becomes the bottom and 12 yards becomes the height.
The area of any triangle is
Area = 1/2 x breadth x height
Area = 1/2 x 5yd x 12yd = 5 x 12/2 = 60/2 = 30yd²
Plumber A charges $50 to come to your house, plus $40 per hour of labor. Plumber B charges $75 to come to your house, plus $35 per hour of
labor. If y is the total dollar amount charged for x hours of labor, which of the following systems of equations correctly represents this
situation?
Answer:
D. y=40x + 50
y=35x + 75
Step-by-step explanation:
x is per hr
it's 40 and 35 dollars per hr
cyrus lives 8 miles due south of adriana. adriana lives 21 miles due west of Jane. jane lives 14 miles due south of madisyn.
the shortest distance between cyrus' house and janes house is:
The shortest distance between Adriana’s house and Madisyn’s house is:
Answer:
Step-by-step explanation:
from Cyrus' to Jane's , the distance is D= [tex]\sqrt{8^{2} +21^{2} }[/tex] = 22.47 mi
from Adriana's to Madisyn's , the dist. is D =[tex]\sqrt{21^{2} +14^{2} }[/tex] = 25.24 mi
Can someone please help me with this
Answer:
(x = 0, y = 0) and (x = 3, y = 0)
Step-by-step explanation:
Let's test out each pair by substituting the values into the inequalities.
Case 1: x = 0, y = 0
0 <= 6
0 < 6
It works!
Case 2: x = -5, y = -15
-15 <= 10 + 6 = 16
-5 + 15 = 10 < 6
It doesn't work.
Case 3: x = 4, y = -2
-2 <= -8 + 6 = -2
4 + 2 = 6 < 6
It doesn't work.
Case 4: x = 3, y = 0
0 <= -6 + 6 = 0
3 < 6
It works!
Case 5: x = 10, y = 0
0 <= -20 + 6 = -14
From here we can already see that it doesn't work
Case 1 and 4 work!
Charlie takes a gymnastic class once a week. At each class, she buys a bottle of water for $0.75 and a protein bar for $2.50. Which of the following expressions represent the amount of money, in dollars, Charlie spends after attending 12 gymnastics classes? Select all that apply.
Answer:
$39
Step-by-step explanation:
[tex]12(.75 + 2.50) = 12(3.25) = 12(3) + 12(.25) = 36 + 3 = 39[/tex]
8. Calir read for 4 hours last week. Luiz
read 6 times as long. Which equation
would show how long Luiz read?
Pls pls pls help me po:)
Bella’s car payment is $321.00 a month for a five year period. What will she have paid for her car when she has paid her finals payment????
Thank you so much !!
Answer:
$19,260
Step-by-step explanation:
1 year = 12 months
5 × 12 = 60
5 years = 60 months
$321 × 60 = $19,260
describe a set of transformations that would map triangle FGH onto F'G'H
Answer:
Describe a set of transformations that would map triangle FGH onto F'G'H
Step-by-step explanation:
answers :
A. 80 degrees
B. 180 degrees
C. 110 degrees
D. 140 degrees
Answer:
D) 140 degrees
Step-by-step explanation:
Radius is perpendicular to tangent line
Draw DA, construction
DA is an angle bisector, m<BAD = 20,
Now, DBA and DCA are congruent right triangles
This is due to LA congruency
90 + 20 + x = 180
x = 70
BDA = CDA
so 70 + 70 = 140
D) 140 degrees
(I'm not that good at geo, so :( )
Please is for 30 points
Mr. Emmer gave a test in his chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. What percent of students would you expect to score between 82 and 90?
Answer:
95.45%
Step-by-step explanation:
Honestly I looked it up I hope it helps though and best of luck! : )
Answer:
47.5% I just took it
The two triangles below have proportional side lengths. Solve for x.
Answer:
90
Step-by-step explanation:
x/15=66/11
x/15=6
multiply by 15 on both sides to get the variable by itself
x=90
Help and you get brainliest
Answer:
1.a) 90 1.b) 32
Step-by-step explanation:
1.) 1^2 + 2^3 + 3^4
Squared means how much times to multiply the same number.
So, 1^2= 1x1=1
2^3=2x2x2=8
3^4=3x3x3x3=81.
So, 81+8+1=90
2. 4^2=4x4=16+2^4=2x2x2x2=16
16+16=32
Please mark me brainliest :)
on a blueprint, the bedroom wall is 6 in long. the scale factor is 1 to 24. what is the length of the actual wall?
A. 144 inches
B. 4 inches
C. 24 inches
D. 6 inches
Answer:
A
Hope This Helps! :)
Answer:
B. 4 inches
Step-by-step explanation:
(24)(1) / 6 = 4
solve the one in the middle asking for f'(10)
From the definition, we have
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{f(x) - f(10)}{x - 10}[/tex]
With [tex]f(x)=\sqrt{x-1}[/tex], we get [tex]f(10)=\sqrt{10-1}=\sqrt9=3[/tex]. So the limit we want to compute is
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{\sqrt{x-1} - 3}{x - 10}[/tex]
Rationalize the numerator by multiplying by its conjugate:
[tex]\displaystyle \frac{\sqrt{x-1} - 3}{x - 10} \times \frac{\sqrt{x-1}+3}{\sqrt{x-1}+3} = \frac{\left(\sqrt{x-1}\right)^2-3^2}{(x-10)\left(\sqrt{x-1}+3\right)} = \frac{x-10}{(x-10)\left(\sqrt{x-1}+3\right)}[/tex]
x is approaching 10, which is to say x ≠ 10, so we can cancel the factors of x - 10 and remove the discontinuity.
Then we're left with
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac1{\sqrt{x-1}+3} = \frac1{\sqrt{10-1}+3} = \frac1{\sqrt9+3} = \frac1{3+3} = \boxed{\frac16}[/tex]
evaluated by direct substitution, which we can do since the limand is continuous.
PRECAL:
Having trouble on this review, need some help.
1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:
[tex]\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}[/tex]
Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.
2. f(x) is continuous at x = -1, so the limit can be computed directly again:
[tex]\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}[/tex]
3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So
[tex]\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}[/tex]
4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.
5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case
[tex]\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}[/tex]
When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.
6. It should be rather clear from the plot that
[tex]\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}[/tex]
because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.
For 7-8, divide through each term by the largest power of x in the expression:
7. Divide through by x². Every remaining rational term will converge to 0.
[tex]\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}[/tex]
8. Divide through by x² again:
[tex]\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}[/tex]
9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:
[tex]\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}[/tex]
10. Factorize the numerator and simplify:
[tex]\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2[/tex]
where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is
[tex]\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}[/tex]
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
Answer:
4 the answer is 4
Step by step explanatin:
Find AB and
BC of this isosceles
triangle.
Answer:
AB = 23, BC = 13
Step-by-step explanation:
[tex]5x - 7 = 23[/tex]
[tex]5x = 30[/tex]
[tex]x = 6[/tex]
AB = 23, BC = 3(6) - 5 = 18 - 5 = 13
Use the diagram above to answer the questions.
a. What are the coordinates of point N? (1 pt.)
b.
Use the Pythagorean Theorem to find the length of
segment PQ. (2 pts)
Answer:
a. (53, 12)
b. I couldn't find this without making a graph myself, hopefully someone will find it or you can figure it out for yourself using the answer I did provide.
Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, D, Sarah travels after hiking for an additional h hours?
Answer:
D=3h+5
Step-by-step explanation:
Given: The rate of increasing speed = 3 miles per hour
The distance she traveled before stopping = 5 miles
Let h represents the number of additional hours for hiking.
Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-
D=3h+5
Answer:
D = 3h + 5
Step-by-step explanation:
The ElA predicts that the United States has 216 billion barrels of crude oil reserves left. If 4 billion barrels are extracted each year, and extraction grows by 0.5% per year, how long will the reserves last?
Anwer o.5
Step-by-step explanation:
because 0.5 x 1 = 0.5
Find the dimensions and solve for the volume.
What is the volume of this prism?
Length: ? Cm
Width: 5 cm
Height: 2 cm
Volume: ? Cm
3
Length is not given or any diagram hasn't been attached.
Length to be taken as x
L=xB=5H=2Now
Volume:-
V=LBHV=5(2)xV=10x cm³What is the approximate area of sector BAC given that 0 ~ 4.71 radians?
A. 117.75m2 or B. 1962.5m2
Answer:
1962.5 m^2
Step-by-step explanation:
area of the entire circle = pi (50^2)
subtract the large area
pi 50^2 - 4.71 /2pi pi 50^2 =
A castle entrance has walls that can be modeled by the equation StartFraction x squared Over 10 squared EndFraction minus StartFraction y squared Over 30 squared EndFraction = 1 with units in feet. How wide is the entrance where the walls are closest together?
10 ft
20 ft
30 ft
60 ft
Answer:
20
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
5.
Step-by-step explanation:
Have you heard of something called reading?
In which number does the digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691?
360,281
486,732
573,674
678,832
HELP GUYS PLEASE!!!!!!!!
Answer:
B. 486,732
__________________________________________________________
SolveTo solve digit problems, multiply the value of the digit example: tens place, hundreds place by 10 to get to the next digit, and then you will have your answer.
[tex]600 * 10 = 6,000~-- > ~thousands~place[/tex]
Therefore, the answer would be B. because it has a 6 in the thousands place.
__________________________________________________________
Questions?Ask in comments.
486,732 is the number in which the digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691. Option B is correct.
To find the number in which the digit 6 has a value that is 10 times as great as the value of the digit 6 in 283,691, we need to compare the place values of the digit 6 in both numbers.
In the number 283,691:
The 6 is in the hundreds place.
Now let us multiply this place with 10.
100×10 = 1000.
Find the number in which the digit is in 1000 place.
In the number 486732, the 6 is in 1000 place.
Hence, Option B is correct. 486,732 is the number in which the digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691.
To learn more on Number system click:
https://brainly.com/question/1763119
#SPJ3
Please help me answer this
Answer:
The answer is B
Step-by-step explanation:
Btw if its wrong im sorry
What is the difference between the mean and the median of the following set of numbers {7, 28, 9, 11, 5}
Answer:
Mean - 12
Median - 9
Mean - Median = 3
Step-by-step explanation:
math