in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equations that are appropriate models for the population of the city, and explain why the others are not
Answer:
[tex]f(x) = 63000(0.97)^x[/tex]
Step-by-step explanation:
Given
[tex]f(0) = 63000[/tex] ---x = 0, in 2012
[tex]f(5) = 54100[/tex] -- x = 5, in 2017
Required
Select all possible equations
Because there is a reduction in the population, as time increases; the rate must be less than 1.
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Where
[tex]b = rate[/tex]
rate > 1 in options (a) and (b) i.e. 1.03
This implies that (a) and (b) cannot be true
For option (c), we have:
[tex]f(x) = 63000(0.97)^x[/tex]
Set x = 0
[tex]f(0) = 63000(0.97)^0 = 63000*1=63000\\[/tex]
Set x = 5
[tex]f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100[/tex]
This is true because the calculated values of f(0) and f(5) correspond to the given values
For option (d), we have:
[tex]f(x) = 52477(0.97)^x[/tex]
Set x = 0
[tex]f(0) = 52477(0.97)^0 - 52477* 1 = 52477[/tex]
This is false because the calculated value of f(0) does not correspond to the given value
For option (e), we have:
[tex]f(x) = 63000(0.97)^\frac{1}{5x}[/tex]
Set x = 0
[tex]f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =[/tex]undefined
This is false because the f(x) is not undefined at x = 0
For option (f), we have:
[tex]f(x) = 52477(0.97)^{5x[/tex]
Set x = 0
[tex]f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477[/tex]
This is false because the calculated value of f(0) does not correspond to the given value
From the computations above, only (c) [tex]f(x) = 63000(0.97)^x[/tex] is true
If you place a 37-foot ladder against the top of a 15-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer:
33.8
Step-by-step explanation:
a²+b²=c²
15²+b²=37²
225+b²=1369
-225 -225
b²=1144
√1144
b=33.8
The distance from the bottom of the ladder to the bottom of the building would be 33.8 foot.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
If you place a 37-foot ladder against the top of a 15-foot building.
Let BC be the distance from the bottom of the ladder to the bottom of the building.
[tex]|AC|^2 = |AB|^2 + |BC|^2 \\15^2+BC^2=37^2\\225 + BC^2=1369\\BC^2 = 1369 - 225\\\\BC^2 = 1144\\\\BC = 33.8[/tex]
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How many miles do you drive to school a statistical or a non-statistical question
Answer:
Non statistical
Step-by-step explanation:
Answer:
Statistical
Step-by-step explanation:
It depends on ones location because any one lives down the street from the local high school.
A non-statistical question only has one answer such as what is the freezing degree mark in Fahrenheit
Pls mark me brainiest
100
75
50
25
what is the slope of this image
Answer:
50
Step-by-step explanation:
Alright, so two of the points are: (0,25) (1,75)
Now we line them up:
(0,25)
(1, 75)
And, 0 to 1 has "1" as a difference.
That'll go on the bottom.
25 to 75 has a "50" difference.
That goes on top.
And then we get the slope of 50.
Hope this helped! :)
Answer:
Slope = 50
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
(1,75) (2,125)
125 - 75/2-1
125-75 = 50
2-1 = 1
50/1 = 50
Divide the difference of 50 and 10 by the sum of 3 and 2. what expression represents the statement?
Answer:
(50-10) ÷ (3+2)
Step-by-step explanation:
Answer:
E
Step-by-step explanation:
E
If both spinners are spun simultaneously, what is the probability that both spinners will land on orange?
Answer:
The probability that neither land on orange is (1/2)* (7/8) = 7/16. Hence, the probability that at least one lands on orange is 1 - 7/16 = 9/16.
Step-by-step explanation:
me big brain
PLSSSSS HELP ME I WILL GIVE BRAINLIEST
Answer:
y-intercept is (0,5)
Step-by-step explanation:
When a graph passes through (0,a), that's y-intercept. y-intercept is a point on y-plane that a graph passes through.
For Ex. If a graph passes through (0,4) then the y-intercept would be (0,4).
But remember that it must be (0,a) for it to be y-intercept (Because it has to intersect the y-plane)
Find the arc length of the partial circle. Use 3.14 for pi and enter your answer as a decimal.
Answer:
However, if you're trying to find the arc length of a partial circle, it's not the same as the circumference of the same circle wholly. You need to find out the circumference of the whole circle first before you can find the arc length (or the circumference of the partial circle).
Step-by-step explanation:
Answer:
9.42 units
Step-by-step explanation:
Find the value of x.
Answer:
x=67º
Step-by-step explanation:
First since the supplementary angle next to 157º is in the triangle, we can find that. 180-157 = 23. Then we can use triangle angle sum theorem to find x. 180-(23+90) = 67º
13. Sarita recorded the high temperatures in her town for the month of July and used
her data to make this box and whisker plot.
The mean temperature of the month was 94".
At least half of the temperatures were 94 or greater.
E
||||
88 90 92 94 96 98 100 102 104
Temperature (°F)
Which statement must be true?
There were fewer temperatures between 92° and 94 than
between 94° and 99%.
There were more temperatures between 99 and 104° than
between 88° and 92,
Answer:b
Step-by-step explanation:
stephen takes a walk around the block. the rectangular block is 125 m long and 75 m wide. How far does Stephen walk?
Answer:
400m
Step-by-step explanation:
It s be the perimeter.
Length X2 sides + width x 2 sides
125 X2 sides + 75. X2 sides
250 + 150
400m
i need help asap, answer with the correct answer and dont troll me
Answer:
B, between 0.1 and 0.3 because between them is 0.2!
A, 0.45 is greater than 0.3 so it a little below would be just right!
Anybody know the answer please?
Answer:
D) 80.5 cm sq
Step-by-step explanation:
square 10x7 = 70
Triangle (7x3) /2 = 10.5
70+ 10.5 = 80.5
PLEASSE, PLZZ HELP MEEEE.
Find the surface area of the ball shown. Use 3.14 for π.
Radius is 11 cm.
Answer:
379.94
Step-by-step explanation:
Hope this helps :)
3. A researcher finds that the correlation between High School GPA and College GPA is 0.40. What
percentage of the variation in College GPA can be explained by the relationship with High School
GPA?
a. 0%
b. 16%
c. 20%
d. 40%
e. 60%
Antoine buys 8 caramel apples for 20.00. Each caramel apple costs the same amount. What is the cost, in dollars, per caramel apple?
Answer:
2.5 per Caramel apple , just divide it , I hope that's correct and I'm sorry if it's not.
Answer:
2 dollars
Step-by-step explanation:
A stem-and-leaf plot is most useful for which reasons below? Select all that apply.
When the measures of central tendency need to be identified.
When the data needs to be displayed in intervals.
When you want to see individual data.
When the range is wide.
Answer:
A,C,D
Step-by-step explanation:
Answer:
ITS ALL OF THEM
JUST DID IT
please please helpppp!
Answer:
3
Step-by-step explanation:
So all of them have a theretical probability of 1/5. Now to determine the experimental propability. (1=6/25, 2=2/25, 3=5/25 or 1/5, 4=4/25, 5=8/25)
Three has an experimental propability of 1/5, which is the same as its theretical propability.
Whats the 32nd term of the following sequence:
5, 8, 11, ...
Need help asp being timed
Answer:
a(x) = √x+3
Step-by-step explanation:
i graphed it on desmos
How do you turn 5(2x+y) into like terms?
5(2x+y) → [ ? ] - 2y-6x
Answer:
10 x + 5 y
Step-by-step explanation:
How many vertices does this shape have?
Solve the equation:
2 + y/3 =8
What is the midpoint of the segment AB given point A(-6.1) and point B(3,7)?
a) (14,6)
b) (7,3)
c) (2,8)
d) (1,4)
I need some help find the area of the shaded region and round to the nearest hundredth
Answer:
The area of the shaded region is 21.45cm².
Find the measure of a.
Answer:
Step-by-step explanation:
The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.
What is the area of the shaded region?
18 mi
19 mi
7 mi
8 mi
Answer
19 mi
Step-by-step explanation:
The range of a set of numbers is 6 1/4
The smallest number is -2 3/8
Work out the largest number.
Answer:
HURRY
Dr. Khan works for the marketing department of a company that manufactures mechanical toy dogs. Dr. Khan has been asked to assess the effectiveness of a new advertising campaign that is designed to be most persuasive to people with a certain personality profile. She brought four groups of participants to the lab to watch the video advertisements and to measure the likelihood that they would purchase the toy, both before and after watching the ad. The results of Dr. Khan’s study are presented below.
Part A
Explain how each of the following concepts applies to Dr. Khan’s research.
Survey
Dependent variable
Big Five theory of personality
Part B
Explain the limitations of Dr. Khan’s study based on the research method used.
Explain what Dr. Khan’s research hypothesis most likely was.
Part C
Use the graph to answer the following questions.
How did the trait of agreeableness affect how people responded to the new ad campaign?
How did the trait of conscientiousness affect how people responded to the new ad campaign?
Answer:
3 [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
To find the largest number add the value of the range to the smallest number.
- 2 [tex]\frac{3}{8}[/tex] + 6 [tex]\frac{1}{4}[/tex] ( change to improper fractions )
= - [tex]\frac{19}{8}[/tex] + [tex]\frac{25}{4}[/tex]
= - [tex]\frac{19}{8}[/tex] + [tex]\frac{50}{8}[/tex]
= [tex]\frac{31}{8}[/tex]
= 3 [tex]\frac{7}{8}[/tex]
A company’s mean salary is $65,000 with a standard deviation of $6,000. What is the probability that an employee makes between $70,000 and $80,000?
An employee has a probability of 0.19706 to make between $70,000 and $80,000
What is Probability?Probability is the potential for an event to occur or occur, and it indicates the likelihood that a statement is true. It is a field of mathematics where the probabilities of experiments happening are computed. We can determine everything from the likelihood of getting heads or tails when tossing a coin to the likelihood of making a research error, for instance, using a probability. It's formula is = number of favorable outcomes/total number of outcomes
Let X be the annual salary of employees in a large company.
Given the mean salary is $65,000 and the standard deviation is $6,000, the probability of making between $70000 and 80000 can be calculated as:
[tex]P(70000 < X < 80000)[/tex] = [tex]P(\frac{70000 - 65000}{6000} < z < \frac{80000 - 65000}{6000} )[/tex]
[tex]P(0.833 < z < 2.5)[/tex]
= 0.99379 - 0.79673 (from normal distribution table)
= 0.19706
Hence, the probability that an employee makes between $70,000 and $80,000 is 0.19706
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