Answer:
1. 45 dollars per year.
2. 49.73 dollars per year.
3. 56.6 dollars per year.
4. Increases
Step-by-step explanation:
Average rate of change
The average rate of change of a function [tex]f(x)[/tex] over an interval [a,b] is given by:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
In this question, we have that:
[tex]A(t) = 900(1.05)^t[/tex]
1. What is the average rate of change for the first year?
[tex]A(0) = 900(1.05)^0 = 900[/tex]
[tex]A(1) = 900(1.05)^1 = 945[/tex]
So
[tex]A = \frac{A(1)-A(0)}{1-0} = \frac{945-900}{1-0} = 45[/tex]
45 dollars per year.
2. What is the average rate of change for the first five years?
[tex]A(0) = 900(1.05)^0 = 900[/tex]
[tex]A(5) = 900(1.05)^5 = 1148.65[/tex]
[tex]A = \frac{A(5)-A(0)}{5-0} = \frac{1148.65-900}{5-0} = 49.73[/tex]
49.73 dollars per year.
3. What is the average rate of change for the first ten years?
[tex]A(0) = 900(1.05)^0 = 900[/tex]
[tex]A(10) = 900(1.05)^{10} = 1466[/tex]
[tex]A = \frac{A(10)-A(0)}{10-0} = \frac{1466-900}{10-0} = 56.6[/tex]
56.6 dollars per year.
4. Does the average rate of change increase or decrease as time from the initial deposit gets longer?
From the previous items, it increases.
are 4x and 15 + x equivalent expressions? Explain your reasoning
Answer:
no.
Step-by-step explanation:
4x means 4 times any given number
15 + x means take any number and add 15.
if x = 2, 4x = 8
if x = 2, 15 + x = 17
Question 1b.
The distribution is...
i. Reasonably symmetric
ii. Abnormal
iii. Highly Skewed
iiii. Bimodel
Answer: i) Reasonably symmetric
=============================================================
Explanation:
The data set is
35,40,45,49,51,54,57,58,58,64,68,68,75,77
Erase the outer pair of values (35 and 77) to end up with this smaller set
40,45,49,51,54,57,58,58,64,68,68,75
Repeat and erase off the outer values (40 and 75) to end up with
45,49,51,54,57,58,58,64,68,68
Keep going until we have either one or two elements left
49,51,54,57,58,58,64,6851,54,57,58,58,6454,57,58,5857,58At this point, we see that the center is between these two last values. So the median is (57+58)/2 = 57.5
--------------------------------
The center is at 57.5
Let L = {35,40,45,49,51,54,57} consist of the set of numbers lower than the median
Let U = {58,58,64,68,68,75,77} be the upper set of values larger than the median.
The middle of set L is 49 and the middle of set U is 68. So Q1 and Q3 are 49 and 68 respectively.
From that, we see the IQR = Q3 - Q1 = 68-49 = 19
Let A and B be the lower and upper fence
We would then say
A = Q1 - 1.5*IQR = 49-1.5*19 = 20.5
B = Q3 + 1.5*IQR = 68 + 1.5*19 = 96.5
Notice how all of the given data values are between A = 20.5 and B = 96.5, which means we don't have any outliers.
Furthermore, if we plotted a box-and-whisker plot (see below), we can see that the two whiskers are fairly the same length. It's not perfect but they're reasonably symmetric. Similarly, the median is somewhat in the middle of the box itself. So this gives a rough idea that the data set we're dealing with is fairly symmetric.
More confirmation can be in the form of a histogram which is also part of the image below. This histogram is fairly symmetric as the left half is nearly (not perfectly) a mirror image of the right half, and vice versa. No one side pulls too far out to create a highly skewed distribution.
3x^2+xy factorise it
Answer:
The factorized expression is [tex]x(3x + y)[/tex]
Step-by-step explanation:
We are given the following expression:
[tex]3x^2 + xy[/tex]
Factorizing:
We place the common factor in evidence.
The common factor of both elements of the sum is x. So
[tex]3x^2 + xy = x(\frac{3x^2}{x} + \frac{xy}{y}) = x(3x + y)[/tex]
The factorized expression is [tex]x(3x + y)[/tex]
What is MA and ABC ifMB = 35° and MC equals 92°
7. Richard deposited $5400 and got back an amount of $6000 after 2 years.
Find Richard's interest rate.
Answer:
600
Step-by-step explanation:
The Difference of 4 and k, divided by 16.
Answer:4-k÷6
Step-by-step explanation:
Aaron rolls a die 40 times. On 25 of those rolls, he has a 3. Michelle rolls a die 80 times. On 40 of those rolls, she has a 6. Which
statement is TRUE about the experimental and theoretical probabilities?
A)The theoretical probability for rolling a 3 is the same as for rolling a 6.
B)The theoretical probability for rolling a 3 is greater than for rolling a 6.
C)The experimental probability for Aaron's tries is the same as Michelle's
tries.
D)The experimental probability for Aaron's tries is less than the experimental
probability for Michelle's tries.
Answer:
Pretty sure its D lemme know if I'm right
PLEASE HELP‼️‼️
A
B
C
D
Answer:
C i think
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
use the side splitter theorem
6/12 = x/18 (replacing AQ with x)
12x = 108 (cross multiply)
x = 9
2/5 g = 3/5 help I don't know what the answer is
Answer:
Step-by-step explanation:
2/5 g = 3/5
g = 3/5 - 2/5 = 1/5
An equilateral triangle has a side length of 10 units. What is its area?
Answer:
Hope my ans help you plz if u can mark me brainlist
Step-by-step explanation:
A = 43.3
The area of an equilateral triangle has a side length of 10 units is 43.3 square units.
What is an equilateral triangle?An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.
Given the side of an equilateral triangle = 10 units
the area is given by,
A = √3/4 × a²
where a is the length of the side,
A = √3/4 × 10²
A = 1.732 x 100/4
A = 43.3 square units.
Therefore, the area of a triangle is 43.3 square units.
Learn more about equilateral triangle;
https://brainly.com/question/3461022
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.A town fair charges $6 for general
admission and $1.50 for each ride. Use
the pattern in the table to find the cost of 7
rides and 10 rides. Then write an equation
for the pattern.
Answer: $1.50r + $6
Step-by-step explanation:
1.50 times 7 is $10.5 without admission
1.50 times 10 is $15 without admission
(R for rides)
so $1.50r + $6 is the equation
The following system of inequalities shows the relationship between two numbers, where the value of x is less than the value of y,
and both numbers are integers.
Which solution is valid within the context of the situation?
Answer:
(-1,5)
Step-by-step explanation:
Evaluate f(4) for the function f(x)=3x-5
A.12
B.7
C.9
D.17
the answer is b.7
Step-by-step explanation:
because you have to plug in the f(4) to the equation like this
f(4)=3(4)-5
and then multiple 3x4 which is 12 then subtract 12 and 5 and you get 7.
Factor the following polynomials: a^2+a+72
Answer:
72 + a (1 + a)
Step-by-step explanation:
Mrs. Bentiez earns $3,400 every month. She spends 25% of her earnings on rent and saves 12% on food, she saves the rest of her money. How much does Mrs. Bentiez save each month?
Answer:
$2244
Step-by-step explanation:
please help 7m - 10 - 4m + 3
Step-by-step explanation:
7m - 10 - 4m + 3
3m-7
Hope it helps
Which repeated series equals 8×10⁴
8×10×4
8×10+10+10+10
8×10×10×10×10
8×4×4×4×4×4×4×4×4×4×4
Answer: 8×10×10×10×10
Step-by-step explanation: Hope this helps :)
Answer:
8×10×10×10×10
Step-by-step explanation:
this one
Have a nice day and I hope I helped you:)
(1 p 18. Demarcus drew a pair of complementary angles. He drew one angle that had a measure of 48º. What was the measure of the other angle he drew? 42° 48° O 132° O 138°
Answer: 42
Step-by-step explanation:
Complementary angles are angles in which the sums equal 90.
90 - 48 = 42.
please help!
Which transformation could NOT be used to prove that two circles are congruent to one another?
a dilation with a scale factor of 2
a dilation with a scale factor of 1
a reflection
a rotation
A transformation which can not be used to prove that two circles are congruent to one another is: A. a dilation with a scale factor of 2.
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
In this context, we can reasonably infer and logically deduce that a dilation with a scale factor of 2 would change the size of the two circle and as such making them incongruent.
In conclusion, a dilation with a scale factor of 1, reflection and rotation can be used to congruency in two circles.
Read more on dilation here: brainly.com/question/20482938
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ANYONE PLEASE JUST HELP ME I HAVE ASKED THE SAME QUESTION 3 TIME BUT NO ONE ANSWERS IT. I WILL GIVE BRAINLEST PLEASE JUST HELP ME.
Answer:
Umm the pic is blocked
Its the blocked picture or meh
Step-by-step explanation:
i need help with everything please if you help you are a legend
Answer:
you got this
Step-by-step explanation:
go with your gut and you sure can win
Answer:
I can help.
Step-by-step explanation:
3a is closer to 1, because 12/12 is 1. and 6/12 is 1/2
3b is closer to 0, because 0/6 is o. and 3/6 is 1/2.
3c is 1 and 1 1/12
11/12 + 1/6
find the common denominator. 12. 6×2 and 1×2 then add straight across.
Which ratio is equivalent to 17:1?
Ο Α.
A. 17
17
0 B. 34 to 2
O C. 1 through 17
D. 1 to 1
Choose 3 values that would make this inequality true: 8 + y ≥ 11
ps help lol
Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1900. How long did each mechanic work?
Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5
Please please help me I have to finish and on question 2
How do I find the x? Please and thank you!
Answer:
x = 9
Step-by-step explanation:
The two opposite interior angles that are opposite to the exterior angle are congruent as shown in the diagram.
Therefore, based on the exterior angle theorem of a triangle, we have the following equation:
2(7x + 2)° = (17x - 23)
14x + 4 = 17x - 23
Collect like terms
14x - 17x = -4 - 23
-3x = -27
Divide both sides by -3
-3x/-3 = -27/-3
x = 9
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer: no solution
Step-by-step explanation:
They have the same slope which means they are parallel lines that will never cross or intersect. This mean that there is no solution
Find the slope of the line that passes through the two points. (-3, -4), (6, 8)
Answer:
Step-by-step explanation:
let (x1 , y1) = ( - 3, - 4) and (x2 , y2) = ( 6 , 8)
Slope (m)
= y2 - y1 / x2 - x1
= 8 + 4 / 6 + 3
= 12 / 9
= 4/3
Answer pls thank you
Answer:
I got 5.19.
Step-by-step explanation:
With this number there is no way to get a perfect sqaure. When you square root it, you get a decimal. If there's an option where it says no perfect square I'd suggest putting that