Step-by-step explanation:
The price of computer = 850
The price of computer after 2 years = 306
By compound depreciation,
[tex]Pn = P (1 - \frac{R}{100} ) ^ T[/tex] ... (i)
where Pn = 306
P = 850
R = rate of interest to be calculated
T = 2( number of years)
substituting the values in equation (1), we get
[tex]306 = 850 (1 - \frac{R}{100} ) ^ 2[/tex]
0.6 = 1 - [tex]\frac{R}{100}[/tex]
R = 40%
The worth after 5 years =
[tex]Pn = 850 (1 - \frac{40}{100} ) ^ 5[/tex]
Pn = 850 (0.077)
= $66.096 = $ 66
The computer be worth after 5 years = $ 66 (option B)
After 5 years, the computer will be worth is $66 (B).
To solve this problem, we'll use the formula for exponential decay, where the rate of decrease is proportional to the value of the computer at that time.
Step 1 :The formula for exponential decay is:
[tex]\[ V(t) = V_0 \times e^{-kt} \][/tex]
Where:
- [tex]\( V(t) \)[/tex] is the value of the computer at time [tex]\( t \)[/tex],
- [tex]\( V_0 \)[/tex] is the initial value of the computer,
- [tex]\( k \)[/tex] is the decay constant, and
- [tex]\( t \)[/tex] is the time in years.
Given:
- [tex]\( V_0 = $850 \)[/tex]
- [tex]\( V(2) = $306 \)[/tex]
We need to find the value of [tex]\( k \)[/tex] using the given information.
[tex]\[ 306 = 850 \times e^{-2k} \][/tex]
Divide both sides by 850:
[tex]\[ \frac{306}{850} = e^{-2k} \][/tex]
Taking the natural logarithm of both sides:
[tex]\[ \ln\left(\frac{306}{850}\right) = -2k \][/tex]
Solve for [tex]\( k \)[/tex]:
[tex]\[ k = -\frac{\ln\left(\frac{306}{850}\right)}{2} \][/tex]
Step 2 :Now that we have [tex]\( k \)[/tex], we can find [tex]\( V(5) \)[/tex]:
[tex]\[ V(5) = 850 \times e^{-5k} \][/tex]
Substitute the value of [tex]\( k \)[/tex] and compute:
[tex]\[ V(5) = 850 \times e^{-5 \times \left(-\frac{\ln\left(\frac{306}{850}\right)}{2}\right)} \][/tex]
[tex]\[ V(5) = 850 \times e^{\frac{5\ln\left(\frac{306}{850}\right)}{2}} \][/tex]
[tex]\[ V(5) = 850 \times \left(\frac{306}{850}\right)^{\frac{5}{2}} \][/tex]
V(5) = 66.61
Therefore, after 5 years, the computer will be worth is $66.
5 2/8-3 7/8=? I need help plzz
Answer:
1 3/8
Step-by-step explanation:
5 2/8 - 3 7/8
= 42/8 - 31/8
= 11/8
= 1 3/8
Make it as the brainliest
Answer:
1 3/8
Step-by-step explanation:
(5 +2/8) -(3 +7/8) = (5 -3) +(2/8 -7/8)
= 2 - 5/8 = 1 3/8
__
It is often convenient to do the arithmetic separately for the integers and the fractions, then combine the results.
Of course, you know that 1 = 8/8 so subtracting 5/8 gives you 3/8.
The equation (x+h)(x+5)=0 has solutions of -5 and 6. What is the value of h.
Answer:
h = -6
Step-by-step explanation:
To solve this problem, plug in the values of either -5 or 6 into the equation for x. Then, simplify. Let's begin by plugging 6 in.
(6 + h)(6 + 5) = 0
I like to use the acronym FOIL for problems like these: first, outside, inside, last.
To start, multiply the first terms, 6 and 6. The answer is 36.
Next, multiply the outside terms, 6 and 5. The answer is 30.
Then, multiply the inside terms, h and 6. The answer is 6h.
Finally, multiply the last terms, h and 5. The answer is 5h.
Add all the products together.
36 + 30 + 6h + 5h = 11h + 66
The equation becomes 11h + 66 = 0.
Now, subtract 66 from both sides to isolate h.
11h = -66
Then, divide both sides by 11 to further isolate h.
h = -6
You have your final answer, h = -6.
How many teenagers should be in the sample
Answer:
THEREFORE
Step-by-step explanation:
THERE SHOULD BE 7 TEENAGERS IN THE SAMPLE.
HOPE, THIS MAY HELP YOU BRO!!..
The sample should include 18 teenagers, as they constitute 60% of visitors aged 13-19 among the total sample of 30.
To determine the number of teenagers that should be in the sample, we first need to calculate the proportion of teenagers among the total visitors and then apply that proportion to the sample size.
From the cumulative frequency table, we can see that:
- The total number of visitors is 350.
- The number of teenagers (ages 13-19) is 210.
The proportion of teenagers among all visitors is:
[tex]\[\frac{\text{Number of teenagers}}{\text{Total number of visitors}} = \frac{210}{350}\][/tex]
Now, we need to apply this proportion to the sample size of 30 to find out how many teenagers should be in the sample:
[tex]\[\text{Number of teenagers in the sample} = \text{Proportion of teenagers} \times \text{Sample size}\][/tex]
[tex]\[\text{Number of teenagers in the sample} = \frac{210}{350} \times 30\][/tex]
[tex]\[\text{Number of teenagers in the sample} = \frac{3}{5} \times 30\][/tex]
[tex]\[\text{Number of teenagers in the sample} = 18\][/tex]
So, there should be 18 teenagers in the sample.
How do the slopes of the lines created by each table compare?
Answer:
The Correct Answer is B
Step-by-step explanation:
Answer:
The correct answer is B. The slope of the Wholesale table is Three-fourths of the slope of the Public table.
Step-by-step explanation:
if an arc of 60 degrees has an arc length of 50pi what is the circumference
Answer: 300[tex]\pi[/tex]
Step-by-step explanation:
Let's use the arc-length formula to solve this problem, and plug in the values that we have. Arc length is 50[tex]\pi[/tex] and the arc is 60°
Arc-length = [tex]2\pi r (\frac{x}{360})[/tex]
[tex]50\pi =2\pi r(\frac{60}{360})[/tex]
Cancel the [tex]\pi[/tex] and simplify the fraction.
[tex]50 = 2r(\frac{1}{6})[/tex]
Simplify further.
[tex]50 = r(\frac{1}{3} )[/tex]
Pass the 3 to the other side.
[tex]150=r[/tex]
So our radius is 150.
To find the circumference, we use the formula [tex]2\pi r[/tex]
Plug in r.
[tex]2\pi (150) = 300\pi[/tex]
To find the full circumference of a circle, multiply the given arc length for 60 degrees (50π) by 6, yielding a total circumference of 300π.
Explanation:To find the circumference of a circle when given the arc length of a particular section, we can use the relationship between the arc's degree measure and the circle's total circumference. Since the arc length of 60 degrees is 50π, we recognize that 60 degrees is one-sixth of a circle's full 360 degrees. Therefore, to find the full circumference of the circle, we multiply the arc length by 6 (because 360° / 60° = 6).
50π times 6 equals 300π, which is the circumference of the circle. This process uses the fact that the circumference of the circle is proportionate to the circle's rotation angle, which completes at 360°, corresponding to an angle of 2π radians.
A restaurant needs four chairs for each table. Let c represent the number of chairs it needs if there are t tables. Which variable is dependent ? Which is independent? Write an equation to represent the relationship, (whoever is the first and has the correct answer gets 100 points and ill give you brainliest. PLEASE I NEED THIS TODAY)
Answer:
DV = numbers of chairs needed (c)
IV = number of tables (t)
IV × 4 = DV OR t × 4 = c
Step-by-step explanation:
DV dependent variable
IV independent variable
brainliest please?
The dependent variable means that it depends on how the independent variable is being manipulated. The independent variable is a variable that represents an amount that is being manipulated.
The dependent variable is "c" because it depends on the number of chairs it needs if there are t tables.
The independent variable is "t" because it manipulates the amount chair there are by the amount of tables there are.
Equation: 4t = c
4t represents the amount of chairs there are for the amount of tables there are. c represents the total amount of chairs.
Best of Luck!
Please help quickly!
Answer: A
Step-by-step explanation:
What is the slope of a line perpendicular to y= -5/6x-7?
a. -6/5
b. 6/5
c. -5/6
d. 5/6
Answer:
it's B
Step-by-step explanation:
Trust me
WHOEVER FINISHES FIRST I WILL MARK AS BRAINLIEST!!!!
Which number is equivalent to 6%? Select all that apply.
A. 6.0
B. 0.06
C. 0.6
D. 6/100
E. 3/50
Answer:
B. 0.06
D. 6/100
E. 3/50
Translate this phrase into an algebraic expression:
500 increased by twice Matt's savings
Use the variable m to represent Matt's savings.
Answer:
500 +2m
Step-by-step explanation:
500 "increased by" "twice Matt's savings"
translates to ...
500 + 2m
__
Your algebraic expression is ...
500 +2m
Answer:
500 + 2m
Step-by-step explanation:
m represents Matt's savings. So 2m is twice that.
500 increased by that means add them, so you get 500 + 2m
Hola cockeroaches, answer this again
Answer:
5- 48
6- 1.5
7-324
Step-by-step explanation: You have to plug in the numbers for the variables
a times c = 12 times 4 =48
1/2 times B= 1/2 times 3= 3/2 = 1/5
A times b times d = 12 times 3 times 9 = 324
SIMPLIFY THE EXPRESSION: 2(4+5v)
PLS HELPPPPP ILL GIVE U BRAINLIEST
Answer:
8+10v
Step-by-step explanation:
Answer:
8+10v
Step-by-step explanation:
Which of the following graphs shows a pair of lines that represent the equations with a solution (−2, 5)?
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the right and 5 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 units to the right and 2 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 places to the left and 2 units up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the left and 5 units up.
Answer:
Substitution.
Step-by-step explanation:
x+y=2
y=-x+2
2x+(-x+2)=4
x=2
(2)+y=2
y=0
Solution: (2,0)
Answer:
subsitution
Step-by-step explanation:
help me with these 3 questions please. aH-
Answer:
1) 2/7; 43; 3/7
2) C
3) 30; 30; 10; is not; 10; is not
Step-by-step explanation:
1) y + 4/7 = 6/7
y = 6/7 - 4/7
y = 2/7
17 + b = 60
b = 60 - 17
b = 43
6/7 = m + 3/7
m = 6/7 - 3/7
m = 3/7
2) 11.5 - x = 5.25
x = 11.5 - 5.25
x = 6.25
3) he can substitute 30 for t.
He can then multiply ⅓ by 30 to get a product of 10 (⅓ × 30 = 10).
Since 15 is not equal to 10, Harry's solution is not correct
What is 7.123 rounded to the nearest whole number?
Find the value of X.
Answer:
x=37
Step-by-step explanation:
We know that the angles in a triangle must add to 180 degrees
So, the three angles: x, 3x-5 and x must be equal to 180
x+3x-5+x=180
Combine like terms
x+3x+x-5=180
5x-5=180
Add 5 to both sides
5x=185
Divide both sides by 5
x=37
Finding Leg Lengths. Find the length of a leg in the 45°-45°-90°
triangle.
Answer:
12. [tex]x=10[/tex]
13. [tex]x=4[/tex]
14. [tex]x=5[/tex]
15. [tex]x=1[/tex]
16. [tex]x=8[/tex]
17. [tex]x=14[/tex]
Step-by-step explanation:
for these i also used the pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex])
[tex]a[/tex] and [tex]b[/tex] are the legs, [tex]c[/tex] is the hypotenuse
12.
[tex]x^{2} +x^{2} =(10\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =200[/tex]
[tex]x^{2} =100[/tex]
[tex]x=10[/tex]
13.
[tex]x^{2} +x^{2} =(4\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =32[/tex]
[tex]x^{2} =16[/tex]
[tex]x=4[/tex]
14.
[tex]x^{2} +x^{2} =(5\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =50[/tex]
[tex]x^{2} =25[/tex]
[tex]x=5[/tex]
15.
[tex]x^{2} +x^{2} =(\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =2[/tex]
[tex]x^{2} =1[/tex]
[tex]x=1[/tex]
16.
[tex]x^{2} +x^{2} =(8\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =128[/tex]
[tex]x^{2} =64[/tex]
[tex]x=8[/tex]
17.
[tex]x^{2} +x^{2} =(14\sqrt{2} )^{2}[/tex]
[tex]2x^{2} =392[/tex]
[tex]x^{2} =196[/tex]
[tex]x=14[/tex]
bonnie runs 1 2/3 times as far as john each day if bonnie runs 5 miles on monday 3 1/2 miles on tuesday and 5 3/4 miles on wednesday how many miles did john run in all those three days
Answer:
3 miles on Monday
2¹/₁₀ miles on Tuesday
3⁹/₂₀ miles on Wednesday
Step-by-step explanation:
We are told that Bonnie runs 1⅔ (⁵/₃) times as far as John each day
This means that John runs ³/₅ times as far as Bonnie.
MONDAY:
Bonnie runs 5 miles on Monday, therefore, John runs:
³/₅ * 5 = 3 miles
TUESDAY:
Bonnie runs 3½ (⁷/₂) miles on Tuesday, therefore, John runs:
³/₅ * ⁷/₂ = ²¹/₁₀ = 2¹/₁₀ miles
WEDNESDAY:
Bonnie runs 5³/₄ (²³/₄) miles on Wednesday, therefore, John runs:
³/₅ * ²³/₄ = ⁶⁹/₂₀ = 3⁹/₂₀ miles
need math help!! answer choices are 80 , 40, 20, and 60
Answer:
60
Step-by-step explanation:
The corresponding angles of the triangles are given, y + 10 and 2y - 40. You need to first find the value of the variable (in this case, y), and to do this, you need to set them equal to one another:
y + 10 = 2y - 40
Subtract y from both sides:
y + 10 = 2y - 40
-y -y
____________
10 = y - 40
Add 40 to both sides:
10 = y - 40
+40 +40
________
50 = y
Now that we have the value of y, you need to plug the value into one of the expressions (either one will come out with the same answer):
y + 10
50 + 10 = 60
OR
2y - 40
2(50) - 40
100 - 40 = 60
Solve the equation if 0 degrees<=x<=360 degrees.
cosx= -1/2
Answer:
Step-by-step explanation:
hello :
cosx= -1/2 0°≤x≤360°
x = 120°
x=240°
Please answer~ 25 points :p
Answer:
y=15
Step-by-step explanation:
We know that the angles in a triangle add to 180 degrees
∠ABC+∠BAC+∠ACB=180
We don't know what ∠ACB is, but we know it is on a straight line with another angle (∠ACD). They are supplementary, and must add to 180
∠ACB+ ∠ACD=180
∠ACB+146=180
Subtract 146 from both sides
∠ACB=34
Now, we know ∠ABC is 4y+8, ∠BAC is 5y+3 and∠ACB is 34, so we can substitute them in
∠ABC+∠BAC+∠ACB=180
4y+8+5y+3+34=180
Combine like terms
4y+5y+8+3+34=180
9y+45=180
Subtract 45 from both sides
9y=135
Divide both sides by 9
y=15
z/8 + 2 = -15
The solution is z = ______.
Look at the attached picture⤴
Hope it will help u..
Answer:
Z = -136
Step-by-step explanation:
z/8 + 2 = -15
-2 -2
Z/8 = -17
Z/8 X 8 -17 X 8
Z = -136
Eve knits scarves for her online store. This week she has already knitted 9 scarves. There are 2 days left in the work week. She set
a goal for herself to knit at least 15 scarves and at the most 21 scarves this week Eve wants to know how many scarves she
should knit each day to meet her goal
Which inequality represents the given situation?
Final answer:
Eve should knit between 3 and 6 scarves each day for the remaining 2 days to meet her goal of knitting at least 15 and at most 21 scarves for the week. The inequality that represents this situation is 3 \<= x \<= 6.
Explanation:
Eve has knitted 9 scarves and wants to knit at least 15 and at most 21 scarves for the week. With 2 days of the workweek left, we need to find out how many scarves she should knit each day to meet her goal. Let's denote x as the number of scarves Eve knits each day for the next two days.
Since Eve has already knitted 9 scarves and wants to knit at least 15, the minimum number of additional scarves she needs to knit is 15 - 9 = 6. So, in 2 days, she must knit at least 6 scarves. This gives us the inequality 2x ≥ 6.
Similarly, the maximum number of scarves Eve aims to knit is 21. Therefore, the maximum number of additional scarves she can knit is 21 - 9 = 12. This leads us to the inequality 2x ≤ 12.
Combining both inequalities, we get 3 ≤ x ≤ 6, which tells us that Eve needs to knit between 3 and 6 scarves each day to meet her goal.
The circumference of a hubcap of a tire is 81.58 centimeters. Find the area of this hubcap
Answer:
Step-by-step explanation:
Answer:
About 530cm²
Step-by-step explanation:
C=2×pi×radius
81.58=2×3.14×radius
81.58=6.28r
81.58÷6.28=6.28r÷6.28
About 12.99cm is radius.
A=pi×radius²
A=3.14×12.99²
A=3.14×168.7401
A=529.843914
Area is about 530cm²
The histograms below show the heights (in meters) of the tallest buildings in China and the United States.
Which pieces of information can be gathered from these histograms?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
The United States has the tallest building of these two countries.
(Choice B)
B
China has more buildings over 390390390 meters tall.
(Choice C)
C
None of the above
Information on the number of tall buildings and their heights in China and the United States can be interpreted from the histograms, with specific focus on the tallest buildings and the number surpassing the 390-meter mark.
Explanation:From the provided histograms comparing the heights of the tallest buildings in China and the United States, several pieces of information can be gathered. If the histograms indicate that the tallest bar on the chart for China is over the 390-meter mark and more numerous compared to the United States' histogram, then Choice B would be correct, indicating that China has more buildings over 390 meters tall. To verify Choice A, we would need to look at the highest point on both histograms; if the highest bar on the U.S. histogram extends further than the Chinese one, then it would mean the United States has the tallest building of the two. Without seeing the histograms, these judgments are based on typical interpretations of histogram data.
When considering data on tall buildings such as the number of stories and their height, constructing a histogram can help illustrate the frequency distribution of these heights. For example, using the rule of thumb that one story is approximately equal to the height of two adult humans, it is possible to establish some basic estimates for building heights. However, for detailed statistical analysis, including the identification of linear relationships or outliers, the data would need a closer examination, possibly using a least-squares or best-fit line.
Which statements are true regarding the sequence below? Check all that apply.
It can be represented using the formula f(x + 1) = 5 (f) when f(1) = 10.
It can be represented using the formula f(x) = 4 6 *.
It can be represented using the formula fx) = 10 (6)*-.
The domain of the sequence is all real numbers.
The range of the sequence is all natural numbers.
It’s a and c
Step-by-step explanation:
The true statements about the given geometric sequence are as follows:
A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.
C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1
What is geometric series?The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The given sequence is as follows:
10/3, 4, 24/5, 144/25, ...
The sequence is a geometric sequence with a common ratio of 6/5.
The first term is 10/3, so we can use the formula f(x + 1) = (6/5)(f(x)) to represent the sequence.
We have
f(x) = 10/3
Also, for f(x+1) we can have
x = 1,
f(1)= 10/3
f(2)= 4
So, f(x + 1) = 6/5(f(x))
Thus, the correct options are A and C.
Learn more about geometric series here:
brainly.com/question/21087466
#SPJ7
The complete question is as follows:
Which statements are true regarding the sequence below? Check all that apply.
10/3, 4, 24/5, 144/25, ...
A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.
B) It can be represented using the formula f (x) = 4 (6/5) /\x.
C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1
D) The Domain of the sequence is all real numbers
E) The range of the sequence is all natural numbers.
Explain how you find the median of a set of date that has an even number of data points.
Answer:
find the average of the 2 numbers in the direct middle.
Step-by-step explanation:
1,2,4,4,4,4,6,6,6,6,6,6
4,6
4+6=10
10/2=
=5
Find the unit rate.
18 books in 3 boxes = (
books per box
Answer:
Step-by-step explanation:15 books in 3 boxes =
books per box
Final answer:
The unit rate of 18 books in 3 boxes is 6 books per box, which is obtained by dividing the total number of books by the total number of boxes.
Explanation:
To find the unit rate of books per box when you have 18 books in 3 boxes, you need to divide the total number of books by the total number of boxes. This is a simple division problem:
Write down the number of books and the number of boxes: 18 books, 3 boxes.Divide the number of books by the number of boxes: 18 \/ 3 = 6 books per box.So, the unit rate is 6 books per box.
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)?
y − 1 = −2(x − 4)
y – 1 = Negative one-half(x – 4)
y – 1 = One-half(x – 4)
y − 1 = 2(x − 4)
Given:
The line parallel to the given line containing the points (-3,3) and (-2,1).
Also, the parallel line passes through the point (4,1).
We need to determine the equation of the line in slope - intercept form.
Slope:
Since, the two lines are parallel, then their slopes are equal.
Thus, the slope of the parallel line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,3) and (-2,1), we get;
[tex]m=\frac{1-3}{-2+3}[/tex]
[tex]m=\frac{-2}{1}[/tex]
[tex]m=-2[/tex]
Thus, the slope of the line is [tex]m=-2[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Since, the line passes through the point (4,1), let us substitute the point (4,1) in the above formula, we have;
[tex]y-1=-2(x-4)[/tex]
Thus, the equation of the line is [tex]y-1=-2(x-4)[/tex]
Hence, Option a is the correct answer.
To find the equation in point-slope form of a line parallel to the given line and passing through a point, we use the fact that parallel lines have the same slope.
Explanation:To find the equation in point-slope form of a line parallel to the given line and passing through the point (4, 1), we need to use the fact that parallel lines have the same slope.
The given line has an equation in point-slope form as y - 1 = -2(x - 4). The slope of this line, which is -2, will be the slope of the parallel line we are looking for.
Using the point-slope form equation y - y1 = m(x - x1), and substituting the values y1 = 1, x1 = 4, and m = -2, we can write the equation as y - 1 = -2(x - 4).
Find the volume of the cylinder the radius is 4ft and the height is 6 ft
Answer:
about 301.59
Step-by-step explanation:
You use the volume formula and just plug in the numbers! Hope that was helpful :)