Answer:
This situation represents [a.) exponential decay
The rate of growth or decay, r, is equal to c.) 0.2
So the value of the computer each year is g.) 80% of the value in the previous year.
It will take [i.) 3 years for the value of the computer to reach $512.
Step-by-step explanation:
Since the value depreciates each year, it represents exponential decay.
The rate of growth or decay, r, is equal to
Depreciates 20%, so r = 0.2.
So the value of the computer each year is ... of the value in the previous year,
Depreciates 20%, so it is 100% - 20% = 80% of the value in the previous year.
It will take x years for the value of the computer to reach $512.
The value of the computer after x years is given by:
[tex]V(x) = V(0)(1-r)^x[/tex]
In which V(0) is the initial value and r is the decay rate. So
[tex]V(x) = 1000(1-0.2)^x[/tex]
[tex]V(x) = 1000(0.8)^x[/tex]
We want to find x for which V(x) = 512. So
[tex]V(x) = 1000(0.8)^x[/tex]
[tex]512 = 1000(0.8)^x[/tex]
[tex](0.8)^x = \frac{512}{1000}[/tex]
[tex](0.8)^x = (0.512)[/tex]
Applying log to both sides:
[tex]\log{(0.8)^x} = \log{(0.512)}[/tex]
[tex]x\log{0.8} = \log{(0.512)}[/tex]
[tex]x = \frac{\log{0.512}}{\log{0.8}}[/tex]
[tex]x = 3[/tex]
So it will take 3 years.
A triangle has a perimeter of 32 inches. The medium side is 7 more than the short side, and the longest side is 3
times the length of the shortest side. Find the shortest side
Answer:
5 inches
Step-by-step explanation:
"perimeter of 32"
a+b+c = 32
a ≤ b ≤ c
"medium side is 7 more than the short side"
b = a+7
"longest side is 3 times the length of the shortest side
c = 3a
Substitution
a + (a+7) + (3a) = 32
5a = 25
a = 5 inches
The downtime per day for a computing facility has mean 4 hours and standard deviation .8 hour. Suppose that we want to compute probabilities about the average daily downtime for a period of 30 days.
i. What assumptions must be true to use the result of Theorem 7.4 to obtain a valid approximation for probabilities about the average daily downtime?
ii. Under the assumptions described in part (i), what is the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours?
Answer:
1
Step-by-step explanation:
Given :
Mean, μ = 4
Standard deviation, s = 0.8
Sample size, n = 30
The distribution is independent.
Z = (x - μ) / s /sqrt(n)
Probability that downtime period is between 1 and 5
P(1≤ x ≤ 5) :
[(x - μ) / (s /sqrt(n))] ≤ Z ≤ [(x - μ) / (s /sqrt(n))]
[(1 - 4) / (0.8 /sqrt(30))] ≤ Z ≤ [(5 - 4) / (0.8 /sqrt(30)]
[-3 / 0.1460593] ≤ Z ≤] 1 / 0.1460593]
P(-20.539602 ≤ Z ≤ 6.8465342)
P(Z ≤ 6.8465342) - P(Z ≤ - 20.5396)
P(Z ≤ 6.8465342) = 1 (Z probability calculator)
P(Z ≤ - 20.5396) = 0 (Z probability calculator)
1 - 0 = 1
What is the approximate distance from one corner of the soccer field to the opposite corner?
60
yards
9.6
100 yards
Answer:
I think Your best answer would be 117 yards.
Step-by-step explanation:
explain how to find 27 percent of 16
Convert 27% to the equivalent decimal 0.27. Multiply 16 by 0.27 to get 4.32. Use estimation to check the answer by choosing the friendly percent 25%. 25% of 16 is equal to 16 ÷ 4 = 4. The answer is reasonable.
4.32
Find the length of the line segment formed by the points (2, 3) and (2, 5)
Answer:
2 units
Step-by-step explanation:
Given data
The points are (2, 3) and (2, 5)
x1= 2
y1= 3
x2= 2
y2= 5
substitute into the distance between two points formula
d=√((x_2-x_1)²+(y_2-y_1)²)
d=√((2-2)²+(5-3)²)
d=√(2)²)
d=√4
d= 2 units
Hence the length is 2 units
Polygon ABCD has the following vertices:
A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)
Calculate the area of the polygon.
28 units squared
38.5 units squared
40.5 units squared
49 units squared
get it right because i can check and i'll not give you brainlyest
:)
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
b = base of the trapezoid = 3 – (-4) = 7
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
A = 38.5
Which property of multiplication is shown?
6 x 5 = 5 x 6
Answer:
Commutative Property of Multiplication
I hope this helps you :D
Commutative
The commutative property tells us that two addition and multiplication sentences are equal no matter the order.
For example:
3+4=4+3
6 x 5= 5 x 6
Hope this helps. Please give brainiest.
1a. Alex skateboards at a constant speed from his house to school 4 miles away. It takes him 15 minutes. What fraction represents his constant speed, C?
the number of customers waiting inside a restaurant was 2 less than a third of those waiting inside. if three customers were waiting inside how many were outside0
Step-by-step explanation:
I think the wording on this problem is incorrect. is one of the insides supposed to be outside
GEOMETRY Find the perimeter of the regular polygon.
3(x - 1)
5x - 6
Answer:
7.5
Step-by-step explanation:
The perimeter of the regular pentagon will be 7.5 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The sides of the regular polygon are 3(x - 1) and (5x - 6). Then the value of the variable x will be
3(x - 1) = 5x - 6
3x - 3 = 5x - 6
2x = 3
x = 1.5
Then the side length of the regular pentagon will be
Side = 3(1.5 - 3)
Side = 3 (0.5)
Side = 1.5
Then the perimeter of the regular pentagon will be
P = 5 x 1.5
P = 7.5 units
The perimeter of the regular pentagon will be 7.5 units.
More about the perimeter of the regular polygon link is given below.
https://brainly.com/question/10885363
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How many groups of 10 are in 60?
Answer:
6
Step-by-step explanation:
10, 10, 10, 10, 10, 10. Those are 6 tens
Siyoni, Adam and Ben share some money in the ratio 5:3:4 In total, Adam and Ben receive $84 Work out how much they cach get. (help me i’ll give brainliest!)
a mechanic rotates the octagonal nut shown clockwise about its center, what is the angle of rotation that moves position 8 to position 5?
Answer:
[tex]Total\ Rotation = 225^{\circ}[/tex]
Step-by-step explanation:
Given
See attachment for nut
Required
Determine the angle of rotation
The total angle in the nut is:
[tex]\theta = 360^{\circ}[/tex]
An octagonal nut has 8 sides. So, each rotation is:
[tex]Each\ Rotation=\frac{360^{\circ}}{8}[/tex]
[tex]Each\ Rotation=45^{\circ}[/tex]
From position 8 to 5, there are 5 movements.
So, the total rotation is:
[tex]Total\ Rotation = Each\ Rotation * Moves[/tex]
[tex]Total\ Rotation = 45^{\circ} * 5[/tex]
[tex]Total\ Rotation = 225^{\circ}[/tex]
The size of a jar of coffee is increased by one 1/5. The new size is later reduced by 1/5
Is the new jar smaller, the same size or larger than the original?
Answer:
Smaller
Step-by-step explanation:
Example: say the original size is 100
increasing 100 by 1/5 is the same as increasing 100 by 20, so the new size is 120
reducing 120 by 1/5 is the same as reducing 120 by 24, so now the new size is 96.
100>96
(GIVING BRAINLYIST) 3 pizzas are shared equally between 10 people. what fraction of a pizza does each person receive. show your work on a image or on paper with using fraction models! thank you for your help :D
Answer:
2 2/5
Step-by-step explanation:
3 pizzas are equal to 24 slices. if there 10 each person can get 2.4 or 2 2/5
Answer:
3/10 of the pizza is given to each person
Step-by-step explanation:
total number of people= 10
number of pizzas=3
as a fraction, this would be 3/10
you can also use this as 30 out of 100 if that's easier to understand.
Hope this helps ༼ つ ◕_◕ ༽つ
solve for the angle x
Answer:
x=75
Step-by-step explanation:
30+x+x=180
2x=150
x=75
I will give the BRAINIEST
Simplify. Write your answer in standard form.
(4x^3+6x-7)+(3x^3-5x^2-5x+9)
Answer:
Step-by-step explanation:
Combine like terms.Like terms have same variable with same exponent
4x³ + 6x - 7 + 3x³ - 5x² - 5x + 9 = 4x³ + 3x³ - 5x² + 6x - 5x - 7 + 9
= 7x³ -5x² + x + 2
2865 students participated in a competitive exam. There were 60 rooms in the
university. Equal number of students were placed in each room. How many students
were not seated in any one of the rooms?
The number of tourists visiting a city doubles every month during the two-month period beginning in Jan, 1st and ending
in Feb, 28th each year, if the number of tourists who visited the city in the beginning of January in that particular year was
x, how many tourists visited the city at the end of February that year?
The number of tourists who visited the city at the end of February that year is 4x.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The number of tourists visiting the city doubles every month, which means the number of tourists at the end of January is 2 times the number of tourists at the beginning of January, or 2x.
Similarly, the number of tourists at the end of February is 2 times the number of tourists at the end of January, or 2(2x) = 4x.
Therefore,
The number of tourists who visited the city at the end of February that year is 4x.
Learn more about expressions here:
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Which organism does not produce an external egg as part of its life cycle? *
1 point
A dog
B turtle
C parrot
D insect
Answer:
dog
Step-by-step explanation:
The Jordan's Michael wanted were on sale for 20% off. The original price of the sneakers is $185.00. How much is the sale? Show your work
The price will be $148. $185 - 20% =$148.
As a salesperson for an electronic parts distributor, you are given two options for your salary structure. The first option has a base salary of $300 a week plus 4% of all sales made. The second option has a base salary of $100 plus 7.5% commission on all sales. Find the sales amount that will result in the two options having the same weekly salary.
Answer:
The amount of sale is approximately 5714.
Step-by-step explanation:
Let x be the sales made that will result to the same salary and let y be the same weekly salary.
We can represent both salaries as follows:
300 + 0.04x = y
100 + 0.075x = y
Subtracting the second equation from the first, we have:
200 – 0.035x = 0
0.035x= 200
x = 200/0.035
x ≈ 5714.
Therefore, the amount of sale is approximately 5714.
Graph -3x+ 5y = -27 HELP ASAP
Answer:
Step-by-step explanation:
I added a screenshot of the graph hope it helps
Select the correct answer.
The branch manager of a clothing store is analyzing the average total bill of sale for his location. The national manager has communicated that
the overall population mean is $45.90 with a standard deviation of $10.3.1. The branch manager has a sample of 400 total bills of sale for his
location. By the central limit theorem, which interval can the branch manager be 95% certain that the sample mean will fall within?
Answer:
We can be 95% certain that the sample mean will fall within $44.87 and $46.93
Step-by-step explanation:
Empirical Rule:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Mean $45.90, standard deviation $10.31.
Sample:
By the Central limit theorem, mean $45.90, standard deviation [tex]s = \frac{10.31}{\sqrt{400}} = \frac{10.31}{20} = 0.5155[/tex]
Which interval can the branch manager be 95% certain that the sample mean will fall within?
By the Empirical Rule, within 2 standard deviations of the mean. So
45.90 - 2*0.5155 = $44.87
45.90 + 2*0.5155 = $46.93
We can be 95% certain that the sample mean will fall within $44.87 and $46.93
HELP! Below is the graph of a polynomial. Which statement about this graph is true?
A. The point (-2,1) is a maximum
B. The point (5,0) is an extreme
C. The point (2,-1.12) is a minimum
D. The point (2,-1.12) is a maximum
Can someone please help me ?????
Answer: 52
Step-by-step explanation:
is that all there is to it? just simply adding up 12 + 32 + 8, adding up the number of women who took the survey? if so, the answer is 52.
1.488 divided by 2.1 rounded to nearest tenth
50 points! Due in 20 minutes! So hurry ! no random answers please. Will mark brainliest:)
13+(x+8) plz i need help
Answer:
21+x
Step-by-step explanation:
Because this does not equal anything, we can't solve for x. Instead, we can just simplify the equation. Since there is a + sign to the left of the parentheses, it shows that we do not need to distribute.
13+(x+8)
21+x
Hope this helps!! Have a nice day ^^
Answer:
First off you would distribute the invisible positive 1 to the x and 8
Then you will get 13+x+8
Last add 13 and 8 to get 21
Your final answer is 21+x
Step-by-step explanation:
Find the nonzero whole number in the definition of "less than" 22<34
Answer:
The inequality is always true.
True
(づ￣ ³￣)づ
is that algebra?
