Answer:
After 2.9 years the town's tax status will change
The towns tax status change within the next 3 years
Step-by-step explanation:
The question below is
Will the towns tax status change within the next 3 years ?
Let
y -----> the population of a small town
t ----> the number of years
we have a exponential function of the form
[tex]y=a(b)^{t}[/tex]
where
a is the initial value
b is the base
In this problem
[tex]a=9,400\ people[/tex]
[tex]b=100\%-14.3\%=85.7\%=85.7/100=0.857[/tex]
substitute
[tex]y=9,400(0.857)^{t}[/tex]
Remember that
The town's tax status will change once the population is below 6,000 people
so
The inequality that represent this situation is
[tex]9,400(0.857)^{t}< 6,000[/tex]
Solve for t
[tex](0.857)^{t}< 6,000/9,400[/tex]
Apply log both sides
[tex](t)log(0.857)< log(6,000/9,400)[/tex]
[tex]-0.067t< -0.1950[/tex]
Multiply by -1 both sides
[tex]0.067t > 0.1950[/tex]
[tex]t > 2.9\ years[/tex]
so
After 2.9 years the town's tax status will change
therefore
The answer is
Yes, the towns tax status change within the next 3 years
the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
To find out after how many years the population of the town would decrease to below 6,000 people, we start with the current population and apply the annual exponential decrease. The population decreases at a rate of 14.3% each year, which means the remaining population each year is 85.7% (100% - 14.3%) of the previous year. Starting with a population of 9,400 people, we need to solve for t in the inequality 9400 × (0.857)^t < 6000. We take the natural logarithm of both sides to solve for t:
ln(9400 × (0.857)^t) < ln(6000)
t × ln(0.857) < ln(6000) - ln(9400)
t > (ln(6000)-ln(9400)) / ln(0.857)
Using a calculator, we find that:
t > 7.17
Therefore, the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
it costs Casey $52.50 to buy 14 gallons of gas. What was the cost per gallon of gas?
Answer:
3.75
Step-by-step explanation:
It would cost Casey $3.75
If you divide 52.50 by 14 you get 3.75
this is a way to find the cost of one gallon
Hope this helps :)
If it does please mark brainliest :D
- A.Hazle <3
Is the orthocenter of a triangle on the inside ?
Answer:
It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross.
Calculate the work done. A tractor pulls a heavy log with a force of 100 pounds. The log moves 3 feet.
1,000 ft-lbs
3,000 ft-lbs
130 ft-lbs
300 ft-lbs
Answer:
300 ft-lbs
Step-by-step explanation:
For work like this,
Just multiply 100 times 3.
You always just multiply the two numbers
Example:
Calculate the work done.
A crane lifts 5,000 newtons to the top of a roof which is 6 meters high.
3,000 ft-lbs
30,000 Nm
5,000 Nm
300 Nm
5,000 x 6 = 30,00
it can also be done like this
5 x 6 = 30
+ 00 = 30,00
The work done is 300 ft-lbs, the correct option is D.
What is the work done?The multiplication of the magnitude of displacement d and the component of the force that is in the direction of displacement is called work done.
Work done is positive when the energy leaves the system. Here, the system is making an effort on the surroundings.
A tractor pulls a heavy log with a force of 100 pounds.
The log moves 3 feet.
The work done is given by;
[tex]\rm Work \ done=Force \times Displacement\\\\Work \ done= 100 \times 3 \\\\Work \ done=300\ ft-lbs[/tex]
Hence, the work done is 300 ft-lbs, the correct option is D.
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In a city the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police station and the fire station?
Answer:
The distance between the police station and the fire station is 4 miles
Step-by-step explanation:
* Lets study the situation in the problem to solve it
- In the city there are three places, library , police station and fire station
- The distance between the library and the police station is 3 miles
less than twice the distance between the police station and the
fire station
- The distance between the library and the police station is 5 miles
* Lets change all of these situation to equations
# Let the distance between the library and the police station is x
# Let the distance between the police station and the fire station is y
∵ The distance between the library and the police station (x) is 3 miles
less than twice the distance between the police station and the
fire station (y)
∴ x = 2y - 3
∵ The distance between the library and the police station is (x) 5 miles
∴ x = 5
- Substitute the value of x in the equation above
∵ x = 2y - 3
∵ x = 5
∴ 5 = 2y - 3 ⇒ add 3 to both sides
∴ 8 = 2y ⇒ divide both sides by 2
∴ 4 = y
∵ y is the distance between the police station and the fire station
∴ The police station is 4 miles apart from the fire station
* The distance between the police station and the fire station is 4 miles
What is the area of the composite figure
Answer: Composite Figures. A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures. That is, a figure is formed by a rectangle and triangle as shown below.
Step-by-step explanation:
Answer:
96
Step-by-step explanation:
Peter bought some bicycles for 4,000 he sold them for 6,200 making $50 on each of the bicycles how many bicycles were there
Answer:
44 bicycles.
Step-by-step explanation:
First we find how much profit he made by subtracting 6200 by 4000. When we do this, we get 2200.
Then, we divide 2200 by 50, because he earned 50 for each bike, which gives us 44.
Answer:
there were 124 bicycles. : )
Step-by-step explanation:
the volume of a cylinder is the base (B) times the length of its height (h).
which of the following is the formula for the volume of a cylinder?
A. V = 1/2Bh
B. V = Bh
C. V = -Bh
D. V = 2Bw
Answer:
[tex]\text{The formula of a volume of a cylinder:}\\\\V=BH\\\\B-base\ area\\H-height\\\\\large\huge\boxed{\bold{B.\ V=Bh}}[/tex]
Answer: [tex]V=B h[/tex]
Step-by-step explanation:
A cylinder is a solid shape having two circular faces connected by a curved surface.
The volume of a cylinder is given by :-
[tex]V=\pi r^2 h[/tex], where r is radius of the base of the cylider and h is height of the cylinder.
Here , the base area of the cylinder is:
[tex]B=\pi r^2[/tex]
Thus, the formula for the volume of a cylinder is given by :-
[tex]V=B h[/tex]
Geometry teacher Plz help me
Check the picture below.
The measure of an angle formed by intersecting secants is half the sum of the measures of the intercepted arcs is: [tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]
The correct option is (B).
The problem step by step:
1. Given Information:
- We have a circle with intersecting secants labeled as A, B, C, and D.
- We need to find the correct equation that describes the relationship between the measures of angles and arcs formed by these intersecting secants.
2. Understanding the Problem:
- When two secants intersect inside a circle, they create several angles and arcs.
- Let's focus on angle[tex]\(m\angle L\)[/tex] and the corresponding arcs AB and CD.
3. Relationship Between Angle and Arc:
- The measure of an angle formed by intersecting secants is half the sum of the measures of the intercepted arcs.
- In other words:
[tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]
4. Answer:
- The correct equation is:
[tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]
Eric wants to sell his car that he paid $7,000 for 3 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, which expression shows how much Eric can sell his car for today?
A.7,000 − 3x
B.7,000 + 3x
C.7,000 − 36x
D.7,000 + 36x
Answer:
Option C. 7,000 − 36x
Step-by-step explanation:
Let
y ----> depreciated value of the car
x---> rate of depreciation
t ----> the time in months
we know that
The linear equation that represent this situation is
y=7,000-xt
For
t=3 years
Convert to months
t=3*12=36 months
substitute
y=7,000-x(36)
y=7,000-36x
simplify the equation 11-1 [19- (2+15)]
Answer: 8
Step-by-step explanation:
11-1 [19- (2+15)]
Step 1: 11-1 (19-17)
Step 2: 11-1+2
Step 3: 11-3
Step 4: 8
Hope it helps!!!
Answer:
Step-by-step explanation:
9
how can e=1/2mv^2 when 1/2 moved to the side of e become 2e? This is because you are trying to find the formula when solved for v.
e = 1/2 mv ^2
Times 2 for both sides.
2e = mv^2
And this is because you are trying to find the formula when solved for v.
And I can help you find that formula which is:
mv^2 = 2e
v^2 = 2e/m
v = √(2e/m)
Does the image represent A function or a relation?
6
4
2
what about this picture/function/expression?
well, we have 3 points over the y-coordinate, but but but, every point has the same x-coordinate, whatever that might be, and so they form a vertical line.
does this straight vertical line pass the vertical line test? nope.
other way to see it is, a function has no x-repeats, the x-coordinate for every point must not be repeated, in this case it is the same for all, so it repeats thrice, so is not a function, just a relation.
12 is 60%, percent of what number?
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
60 is a percent and percents are always taken out of the 100. This means that one proportion will have 60 as the part and 100 as the whole
We want to know out of what number is 12 60%. This means 12 is the part and the unknown (let's make this x) is the whole
[tex]\frac{12}{x} =\frac{60}{100}[/tex]
Now you must cross multiply
12*100 = 60*x
1200 = 60x
To isolate x divide 60 to both sides
1200/60 = 60x/60
20 = x
This means that 60% of 20 is 12
Hope this helped!
~Just a girl in love with Shawn Mendes
The number that 60% of 20 is 12.
We know that 60 is a percent and percent is always taken out of the 100. which means that one proportion will have 60 as the part and 100 as the whole
We need to know out of what number is 12 60%. This means 12 is the part and the unknown, x is the whole
Now we must cross multiply;
12*100 = 60*x
1200 = 60x
To isolate x divide 60 to both side;
1200/60 = 60x/60
20 = x
This, means that 60% of 20 is 12
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use the squared identities to simplify 2 cos^2 x cos^2 x
Answer:
Option A
Step-by-step explanation:
Which graph shows the solution to the inequality -3x-7 <20?
Answer:
Graphs..?
Step-by-step explanation:
For this case we must indicate the graph of the following inequality:
[tex]-3x-7 <20[/tex]
We add 7 to both sides of the inequality:
[tex]-3x <20 + 7\\-3x <27[/tex]
We divide between -3 to both of the inequality taking into account that the meaning changes:
[tex]x> \frac {27} {- 3}\\x> -9[/tex]
Answer:
[tex]x> -9[/tex]
See attached image
Which of the following number sentences is an example of the identity property of addition?
16 × 0 = 0
8 + 0 = 8
1 × 4 = 4
1 + 11 = 11 + 1
The solution to an inequality is (–∞, 6.5]. Is 6.5 a solution to the inequality? Explain your answer.
The closing bracket ']' in the inequality solution set (–∞, 6.5] indicates that 6.5 is included, making it a solution to the inequality.
The solution to an inequality is (–∞, 6.5]. To determine if 6.5 is a solution to the inequality, we look at the notation used. The parenthesis '(' indicates that the number at this end of the interval is not included in the solution set, while the bracket ']' indicates that the number at this end is included. Since 6.5 is associated with a closing bracket, it means that 6.5 is indeed a solution to the inequality. Therefore, any number less than or equal to 6.5 is a solution to this particular inequality.
The correct explanation among the given options is the following:
"The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5."
In interval notation, brackets ([ and ]) indicate that the endpoint is included in the solution, while parentheses (( and )) indicate that the endpoint is not included.
Here, with (-∞, 6.5], the closing bracket means 6.5 is included in the solution to the inequality.
Thus, 6.5 is a valid solution to the inequality.
The complete question is : The solution to an inequality is (-, 6.5]. Is 6.5 a solution to the inequality? Explain your answer
The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the salution does not
include 6.5. The solution includes numbers from 6.5 to infinity. Because a parenthesis is used, the solution does not include 6.5.
The solution is the point(, 6.5). Because a bracket is used, 6.5 is a solution to the inequality.
The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5.
The lines graphed below are parallel.the slope of the slope of red line is 2/5 .what is the slope of the green line
Answer:
[tex]\large\boxed{\text{the sloe}\ m=\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
[tex]\text{We have the slope}\ m_1=\dfrac{2}{5}.\\\\\text{The slope of parallel line is the same:}\ m_2=\dfrac{2}{5}[/tex]
an equation for a line in the plane allows you to find x- and y-coordinates of any point on that line true or false?
Answer:
True
Step-by-step explanation:
When you are given an equation of a line in the plane, it´s like if they´ve given you the map to a line, and in this case it´s really easy to calculate the value of the different points on X and Y and by that you just have to immagine a value for one of the variables to calculate the other one, most cases is always X the one that you give the value to, and then you just calculate the Y.
Answer:
True.
Step-by-step explanation:
An equation for a line in the plane allows you to find x- and y-coordinates of any point on that line.
a community group sells 2000 tickets for its raffle. the grand prize is a car. neil and 9 of his friends buy 10 tickets each. when the winning number is announced, it is found to belong to neil's group. given the information, what is the probability that the ticket belongs to neil?
Answer:
1/10
Step-by-step explanation:
how can the correlation in the scatter plot graph below best be described?
positive correlation
negative correlation
both positive and negative
no correlation
Answer:
Option B is correct
Step-by-step explanation:
The graph represent the negative correlation.
In negative correlation there is inverse relationship between two variables. If value of one variable is increasing then the value of other variable is decreasing.
As seen from the graph when the value of x is increasing the value of variable y is decreasing
So, Option B negative correlation is correct.
what is x + 1 = 9 ?? fill in the x
Answer:
x=8
Step-by-step explanation:
Cause 8+1 =9
Answer:
8
Explanation:
to get the answer we have to use the opposite of addition which is subtraction. we flip around the equation so now it would be 9 - 1 = ?
9 minus 1 is 8.
that is how you get the answer.
find the weight in pounds of a 140-kilogram person. Round to the nearest hundredth
Answer:
308.65 Pounds
Step-by-step explanation:
Since one kilogram is 2.20462 pounds you can multiply 140 by 2.20462 to get 308.6468 and rounded to the nearest hundredth it would be 308.65.
The weight of a 140 kilogram person in pounds is approximately 308.64 pounds, when rounded to the nearest hundredth.
Explanation:To find the weight of a 140-kilogram person in pounds, we first need to understand that weight is a measure of the force of gravity on an object and can be calculated by multiplying the mass of the object by the acceleration due to gravity.
However, here, we are converting kilograms to pounds, which is a conversion of mass units, not weight. The conversion factor from kilograms to pounds is approximately 2.2046.
Therefore, to convert 140 kilograms into pounds, we multiply 140 by 2.2046:
140 kg * 2.2046 = 308.644 pounds.
And rounded to the nearest hundredth, we get 308.64 pounds.
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Question is in the picture
Answer:
i cant see the picture
Step-by-step explanation:
What would be the surface area of the prism if the length of each side is cut in half?
A)165 square centimeters
B)178 square centimeters
C)181 square centimeters
D)362 square centimeters
11/2 = 5.5
10/2 = 5
12/2 = 6
SA = 5.5 x 5 x 2 + 5.5 x 6 x 2 + 5 x 6 x 2
SA = 55 + 66 + 60
SA = 181
The answer is C) 181 cm²
Correct Option is C , 181 square cms.
l = 11cm
b = 10cm
h = 12cm
Surface Area of Cuboid:
A cuboid has 6 rectangular faces, the surface area of the whole cuboid is the sum of 6 rectangular surface areas of cuboid.
surface area = l x b + b x h + h x l + l x b + b x h + h x l
Surface area of cuboid = 2 x ((l x b) + (b x h) + (h x l))
When the length of each side is cut in half so, l, b and h decreases by 2.
l = [tex]\frac{l}{2}[/tex] = [tex]\frac{11}{2}[/tex] = 5.5cm
b = [tex]\frac{b}{2}[/tex] = [tex]\frac{10}{2}[/tex] = 5cm
h = [tex]\frac{h}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6cm
Surface Area of the cuboid = 2 x ((l x b) + (b x h) + (h x l))
=> 2 x ((5.5 x 5) + (5 x 6) + (6 x 5.5))
=> 2 x (27.5 + 30 + 33)
=> 2 x (90.5)
=> 181 [tex]cm^{2}[/tex]
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Factories 24x^2-41x+12
Answer:
(3x - 4)(8x - 3)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 24 × 12 and sum = - 41
The required factors are - 32 and - 9
Use these factors to split the x- term
24x² - 32x - 9x + 12 ( factor the first/second and third/fourth terms )
= 8x(3x - 4) - 3(3x - 4) ← factor out (3x - 4) from each term
= (3x - 4)(8x - 3) ← in factored form
Which of the following values have 3 significant figures? Check all that apply.
A. 10.1
B. 100.05
C. 120
D. 129
Answer:
A.
Step-by-step explanation:
To find a significant figure you just count how many numbers are before and after the decimal place but if the first number is zero then it does not count.
Final answer:
The values with 3 significant figures are A. 10.1 and D. 129, as non-zero numbers are always significant, and there are no leading, captive, or trailing zeros to consider in these cases.
Explanation:
The values that have 3 significant figures are:
A. 10.1
D. 129
In A, all the digits are significant because they are all non-zero numbers. In D, similarly, all digits are significant since non-zero numbers are always counted as significant figures.
For the options not chosen:
B. 100.05 has 5 significant figures because zeros between non-zero numbers are significant and so are the ending non-zero numbers.
C. 120 may be seen as having 2 or 3 significant figures depending on whether the zero is considered significant; additional context such as writing the number in scientific notation or a decimal point (120.) is needed to clarify its significance.
Find the savings balance after 9 months with an APR of 4% and monthly payment of $250.
Answer:
$ 2533.594
Step-by-step explanation:
The saving balance is found by the equation;
[tex]SV=P*[((1+i)^n -1)/i][/tex]
where P=monthly payments, i= interest rate n=period
Given ;
P= $250 n=9months and i=6%(0.04) per year, find savings balance?
Note than n is given in months so we divide the rate by 12 i.e
0.04/12 =0.003
Substitute values in the formulae;
SV= 250 × [((1+0.003)^9 - 1)/0.003)]
[tex]SV= 250* [((1+0.003)^9 -1 )/0.003]\\\\SV=250*[(1.003)^9 -1)/0.003]\\\\SV=250*[(1.0304 -1)/0.003]\\\\SV=250*[0.0304/0.003]\\\\SV=250*10.134\\\\SV=2533.594[/tex]
True or False ? The distance formula is equivalent to the Pythagorean theorem if you are
trying to find the distance between a point in the plane and the origin.
I believe that it is true due to it, the distance formula uses x and y coordinates. So, they're the same thing in two different types, or so..
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Which expressions are equivalent to K/2
Choose 2 answers:
A k-2
B 2/k
C 1/2k
D k/2
E k+k
Answer:
C and D
Step-by-step explanation:
D is the exact same.
For C this is already proven but you can test this by choosing any number for K (4) and multiply it by 1/2. You get 2 which is the same as 4/2.
The expression which is equivalent to the expression, K/2 is; Choice D: k/2.
According to the question;
We are required to determine the expression which is equivalent to k/2.Among the choices; Choice D: k/2 is the exact same as the expression K/2.
However, Choice C if written as (1/2)k is equivalent to k/2 as they both mean half of k.
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