Answer:
(A): As year increases the number of pikas reduces.
(B): As year increases the number of pikas increases as opposed to when the rate reduces.
Step-by-step explanation:
See comment for complete question
Given
[tex]a = 144[/tex] --- Initial Population
[tex]r = 8\%[/tex] --- rate
(A) WHEN THE RATE DECREASES
First, we need to write out the function when the population decreases.
This is given as:
[tex]f(x) = a(1-r)^x[/tex]
Substitute values for a and r
[tex]f(x) = 144(1-8\%)^x[/tex]
Convert % to decimal
[tex]f(x) = 144(1-0.08)^x[/tex]
[tex]f(x) = 144(0.92)^x[/tex]
Next, we calculate the average rate of change for both intervals using:
[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]
For 1 to 5:
[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]
[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]
Calculate f(5) and f(1)
[tex]f(x) = 144(0.92)^x[/tex]
[tex]f(1) = 144*0.92^1 =144*0.92=132.48[/tex]
[tex]f(5) = 144*0.92^5 =144*0.66=95.04[/tex]
[tex]Rate = \frac{95.04 - 132.48 }{4}[/tex]
[tex]Rate = \frac{-37.44}{4}[/tex]
[tex]Rate = -9.36[/tex]
For 6 to 10:
[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]
[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]
Calculate f(6) and f(10)
[tex]f(x) = 144(0.92)^x[/tex]
[tex]f(6) = 144*0.92^6 =144*0.61=87.84[/tex]
[tex]f(10) = 144*0.92^{10} =144*0.43=61.92[/tex]
[tex]Rate = \frac{61.92-87.84}{4}[/tex]
[tex]Rate = \frac{-25.92}{4}[/tex]
[tex]Rate = -6.48[/tex]
So, we have:
[tex]Rate = -9.36[/tex] for year 1 to 5
This means that the number of pikas reduces by 9.36 yearly
[tex]Rate = -6.48[/tex] for year 6 to 10
This means that the number of pikas reduces by 6.48 yearly
So, we can say that, as year increases the number of pikas reduces.
(B) WHEN THE RATE INCREASES
First, we need to write out the function when the population decreases.
This is given as:
[tex]f(x) = a(1-r)^x[/tex]
Substitute values for a and r
[tex]f(x) = 144(1+8\%)^x[/tex]
Convert % to decimal
[tex]f(x) = 144(1+0.08)^x[/tex]
[tex]f(x) = 144(1.08)^x[/tex]
Next, we calculate the average rate of change for both intervals using:
[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]
For 1 to 5:
[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]
[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]
Calculate f(5) and f(1)
[tex]f(x) = 144(1.08)^x[/tex]
[tex]f(1) = 144(1.08)^1 = 144*1.08= 155.52[/tex]
[tex]f(5) = 144(1.08)^5 = 144*1.47= 211.68[/tex]
[tex]Rate = \frac{211.68 - 155.52}{4}[/tex]
[tex]Rate = \frac{56.16}{4}[/tex]
[tex]Rate = 14.04[/tex]
For 6 to 10:
[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]
[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]
Calculate f(6) and f(10)
[tex]f(x) = 144(1.08)^x[/tex]
[tex]f(6) = 144(1.08)^6 = 228.52[/tex]
[tex]f(10) = 144(1.08)^{10} = 310.89[/tex]
[tex]Rate = \frac{310.89-228.52}{4}[/tex]
[tex]Rate = \frac{82.37}{4}[/tex]
[tex]Rate = 20.59[/tex]
So, we have:
[tex]Rate = 14.04[/tex] for year 1 to 5
This means that the number of pikas increases by 14.04 yearly
[tex]Rate = 20.59[/tex] for year 6 to 10
This means that the number of pikas increases by 20.59 yearly
So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.
A(n)______ contains variables,numbers, and at least one operation.
Answer:
algebraic expression. An expression that contains at least one variable, at least one numbers and at least one operation.
Step-by-step explanation:
Answer:
expressions
Step-by-step explanation:
this is how a definition in a textbook would be written. they just put a blank in
please answer the question bellow, i'm so confused lol
Answer:
12
Step-by-step explanation:
find the lcm between 6 and 4
Answer:
He will wear both on the 12th day.
Step-by-step explanation:
Find the LCM (Least Common Multiple) of 4 and 6.
Prime factor both numbers:
4 = 2²
6 = 2 · 3
LCM = 2² · 3
= 12
To find the LCM, take the greatest common numbers (2² and 3) and multiply them.
This method works well with very big numbers.
DEF is a right angled triangle calculate the length of EF correct to 3 sigificant figures
Answer:
[tex]\displaystyle EF \approx 15.9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
Angle θ = 28°
Adjacent Leg = EF = x
Hypotenuse = DF = 18
Step 2: Solve for x
Substitute in variables [Cosine]: [tex]\displaystyle cos28^\circ = \frac{x}{18}[/tex][Multiplication Property of Equality] Multiply 18 on both sides: [tex]\displaystyle 18cos28^\circ = x[/tex]Evaluate trig: [tex]\displaystyle 18(0.882948) = x[/tex]Multiply: [tex]\displaystyle 15.8931 = x[/tex]Rewrite: [tex]\displaystyle EF = 15.8931[/tex]Round: [tex]\displaystyle EF \approx 15.9[/tex]True or False? If one of the angles of a triangle is obtuse, then the triangle is obtuse.
Answer:
True
Step-by-step explanation:
Image result for True or False? If one of the angles of a triangle is obtuse, then the triangle is obtuse.
In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°. Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. ... Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.
Answer:
True, as long as the other angles are acute !!
Step-by-step explanation:
I hope this helps !! :D
Jen rode her bike 15of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Answer:
2.4MPH
Step-by-step explanation:
Use the principle of rate x time:
(1/5)*5=1
1 mile per 25 minutes= 2.4 mph
MARK AS BRAINLIEST
CONVERTING METRIC UNITS - LENGTH WEIGHT & VOLUME 1
2)
2 kg =
B
1)
1 kg =
g
4)
2 cm =
mm
3)
1 cm =
mm
6)
2 km =
m
5)
1 km =
m
8)
2 L =
ml
7)
1 L =
mL
10)
2 m =
cm
9)
cm
1 m =
Which is the most? Circle the largest amount in each box.
1 L
1 m
560 m
2,000 cm
1 kg
1,250 mL
80 cm
300 g
980 mL
1 km
120 mm
950 g
greater than (>), less than (<) or equals (=) to compare the amounts.
2)
1 m
75 cm
590 mL
1L
1 km
250 m
2 cm
4)
20 mm
7 cm
50 mm
2 m
6)
250 cm
4 m
350 cm
8)
1 kg
-,200 g
10)
3m
2 L
20 mL
300 cm
12)
500
Om
1 km
4 kg
Answer:
2 KM 2 L 2 KG I dont know the rest i figured i could help someone but thats all i can do at the moment sorry i might come back to finish it later.
Step-by-step explanation:
If anyone can answer these questions that would help a lot. Besides 13 and 14
Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression, when many banks lost their customers’ deposits, she is worried that the bank might not keep her money safe. Give Mary some recommendations about what she can do to make sure that her money stays protected.
Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.
determine if JK and LM parallel, perpendicular, or neither .
Answer:
3 - Perpendicular.
4 - Parallel.
Step-by-step explanation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]JK = \frac{1-(-7)}{-4-(-10)} = \frac{8}{6} = \frac{4}{3}[/tex]
[tex]LM = \frac{-2-2}{-6-(-3)} = \frac{-4}{3}[/tex]
Perpendicular, because two lines are considered perpendicular if their slopes are opposite reciprocals.
[tex]JK = \frac{-2-(-2)}{3-11} = \frac{0}{-8} = 0[/tex]
[tex]LM = \frac{-2-(-7)}{1-1} = \frac{5}{0} = 0[/tex]
A rectangle with length 3 1/2 ft and width 2 1/4 ft what is the area
Answer:
Step-by-step explanation:
Hope this helps
click link
Answer: 5 2/6
Step-by-step explanation:
first come first served:)
Answer:
2.
gold beads to silver beads
table: 6:9 12:18 24:36 30:45
equivalent ratios: 4:6 10:15 20:30 100:150
3.
A.33
B.1.2
Step-by-step explanation:
2.
the rule is, gold beads x 1 1/2 = silver beads
3.
A. 165/5=33
B.9.60/8=1.2
hope this helps have a blessed day :)
Please help!!!!!!!
thank you for helpingggggg
Answer:
x = 9
Step-by-step explanation:
5x * 135 = 180
180 - 135 = 45
5x = 45
5 ÷ 5 = 0
45 ÷ 5 = 9
X = 9
Please help ten points
The price of a television is $567.31. The state sales tax rate is 8.3%.
What is the total cost of the television?
that in the image could be your answer but i rlly dont know thats the way I was taught
Pencils come in packages of 10 . Erasers come in package of 12 . Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil . How many packages of pencils and erasers should Phillip buy ?
Answer: 60
Step-by-step explanation:
From the question, we are informed that pencils come in packages of 10 while erasers come in package of 12 .
We are further told that Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil, this simply means that we have to calculate the lowest common multiple for 10 and 12.
Multiples of 10 = 10, 20, 30, 40, 50, 60,
Multiples of 12 = 12, 24, 36, 48, 60, 72
Therefore, the packages of pencils and erasers that Phillip should buy will be 60
I need help with geometry really bad, if you don’t mind answering this? And also if your good at geometry drop your number so I can get help
Answer:
127
Step-by-step explanation:
using the definition of a straight angle:
53+x=180
127
Matti rolled the six-sided number cube once, tossed the coin once, and flicked the spinner one time.
How many total possible outcomes are there if she does all three at the same time?
Answer:
60 outcomes
Step-by-step explanation:
6 x 2 x 5
60 possible outcomes are there if she does all three at the same time.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Given:
Matti rolled the six-sided number cube once,
tossed the coin once,
and flicked the spinner one time.
So, the possibilities of doing three at the same time
= 6 x 2 x 5
= 60
Hence, there are 60 possible ways.
Learn more about combination here:
https://brainly.com/question/13387529
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In a recent survey of 655 working americans ages 25-34, the average weekly amount spent on lunch was $43.29 with standard deviation $2.75. The weekly amounts are approximately bell-shaped
Answer:
99.7%
Step-by-step explanation:
Given that:
sample size (n) = 655
sample mean ([tex]\overline x[/tex]) = 43.29
Standard deviation [tex]\sigma[/tex] = 2.75
Let's assume we are to estimate the percentage between $33.72 and $51.54
Then;
The test statistics at 33.72 is :
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]Z = \dfrac{33.72 -43.29}{2.75}[/tex]
[tex]Z = -3.48[/tex]
Z at 51.54
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]Z = \dfrac{51.54 -43.29}{2.75}[/tex]
[tex]Z = 3.00[/tex]
Using the empirical standard rule, the percentage will be 99.7%
When a number is increased by 9.5%, the result is 58. What is the original number to the nearest tenth?
(I've seen other questions like this, but the answer is wrong. It's not 50 or 52.49 or 52.5.)
Answer:
53
Step-by-step explanation:
58÷1.095= 53 is the answer
Answer:
5.03196347032
Step-by-step explanation:
We do:
.095x+x=58
1.095x=58
x=52.96
52.96 is a approximation and when you do the math and see what 9.5 of 52.96 plus 52.96 is you get 57.9912 which is super close to 8 The exact answer is x = 5.03196347032
Evaluate the expression when x = 2.5 and y = 6.
5xy
Answer:
75
Step-by-step explanation:
5(2.5)(6)
5*2.5*6
=75
Answer:
75
Step-by-step explanation:
5*(6x2.5)
6x2.5=15
15x5=75.
NEED HELP ON HOMEWORK ASAP
Answer:c
Step-by-step explanation:
3*1= 3 3*2=6 and so on
Gilbert took 2 hours longer to drive 240 miles on the first day of a business trip than to drive 144 miles on the second day. If his rate was the same both days, what was his driving time for each day?
Answer:
dyvhbCNN mfg beneficialgVCR specializations acknowledgement
If f(x)=3x-2 and g(x)=2x+1 find (f-g)(x)
9514 1404 393
Answer:
(f-g)(x) = x -3
Step-by-step explanation:
(f-g)(x) = f(x) -g(x)
= (3x -2) -(2x +1)
= 3x -2 -2x -1 = (3x -2x) +(-2 -1)
(f-g)(x) = x -3
The y-intercept is the point where the line crosses the
A. origin
B. slope
C. y-axis
D. x-axis
the product of 9 and c
Answer:
The answer is 9c or 9 × c..
Rayann has 4 bracelets , Jennifer has 8 bracelets, June has 3 bracelets, and Tammy has 5 bracelets. They want to redistribute the bracelets so that each girl has the same number of bracelets. If the bracelets are redistributed, how many should each girl get?
Answer:
B) 5
Step-by-step explanation:
They have a total of 4+8+3+5 = 20 bracelets
There is 4 girls
20/4 = 5
Which whole numbers does the square root of 104 falls in between?
Answer:
10 and 11
Step-by-step explanation:
The square root of 104 is 10.1980390272. This falls between the whole numbers 10 and 11.
PLEASE THIS IS MY THIRD TIME ASKING TODAY I NEED HELP!!!
please only answer if you know how to do this!
Answer:
The answers are:
Step-by-step explanation:
1)Adjacent
2)Vertical
3)Corresponding
4)None of these
5)1,7 3,5 4,6 2,8 (<--angle numbers)
6)4,5 2,7 (<--angle numbers)
7)1=85, 2=95, 3=85, 4=85
8)1=60, 2=120, 3=60, 4=120
9)1=90, 2=90, 3=90, 4=90
10) No, they are not parallel. A protractor would show that the intersection angles are different, meaning the lines aren't parallel.
SORRY it took so long hope this helps!!
Answer:
1.
adjacent
2.
vertical
3.
corresponding
4.
none (just regular interior and thats not an option)
5.
(<5,<7) (<6,<8) (<1,<3) (<2,<4)
6.
(<2,<7) (<6,<3)
7.
<1= 85
<2= 95
<3= 85
<4= 85
8.
<1= 60
<2= 120
<3= 60
<4= 120
9.
<1= 90
<2= 90
<3= 90
<4= 90
10. No, its not parallel because the corresponding angles 1 and 7 aren't equal. You can use a protractor to figure this out by finding the measurement of angles 1 and 7. Because they aren't equal degrees, the lines will cross at some point
Trapezoid KLMN has vertices K(1, 3), L(3, 1), M(3, 0), and N(1, −2).
Is this trapezoid an isosceles trapezoid?
Select from the drop-down menu to correctly complete the statement.
Trapezoid KLMN
is not
an isosceles trapezoid.
Answer:
Yes, the trapezoid is an isosceles trapezoid.
As the diagonals of the trapezoid KLMN are not equal in length it is not an isosceles trapezoid.
What is the area of a trapezoid?The area of a trapezoid is the average length of the parallel sides times the height.
We know isosceles trapezoids have equal legs length and diagonals are also of the same length.
Given a trapezoid KLMN with verticies K(1, 3), L(3, 1), M(3, 0), and N(1, −2).
∴ KM and LN are two diagonals of the trapezoid and if KM = LN then it is an isosceles trapezoid.
To determine if KM and LN are equal or not we'll simply use the distance formula which is,
D = [tex]\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex].
∴ KM = [tex]\sqrt{ (3 -1)^2 + (0 - 1)^2}[/tex].
KM = [tex]\sqrt{ (2)^2 + (-1)^2}[/tex].
KM = [tex]\sqrt{5}[/tex].
And LN = [tex]\sqrt{ (1 -3)^2 + (-2 - 1)^2}[/tex].
LN = [tex]\sqrt{ (-2)^2 + (-3)^2}[/tex].
LN = [tex]\sqrt{ 4 + 9}[/tex].
LN = [tex]\sqrt{13}[/tex].
∴ KM ≠ LN hence diagonals are not equal.
learn more about trapezoids here :
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AB=
Round your answer to the nearest hundredth
Answer:
Step-by-step explanation:
2/sin25=AB/sin90
AB=4.73
