Answer: f(x) = 90,200 (1-.002)^7
Step-by-step explanation:
f(x) = a (1 - r)^t
a - initial amountr - ratet - timef(x) = 90,200 (1-.02)^7
The equation f(7) = 90,200 (1 - 0.02)⁷ represents the town’s population after 7 years.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
A town has a population of 90,200 and shrinks at a rate of 2% every year.
As we know the exponential equation for the population as
f(n) = a (1 - r)ⁿ
Where a is the initial population
r is rate
n is years
As per the question, we have
a = 90,200, r = 2/100 = 0.02, and t = 7 years
Substitute the known values in the above equation, and we get
f(7) = 90,200 (1 - 0.02)⁷
This equation represents the town’s population after 7 years.
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Can someone help me please!!?
Answer:
AB = 21
Step-by-step explanation:
the line EB is parallel to the side of the triangle DC and intersects the other 2 sides proportionally , that is
[tex]\frac{AE}{ED}[/tex] = [tex]\frac{AB}{BC}[/tex] ( substitute values )
[tex]\frac{14}{12}[/tex] = [tex]\frac{AB}{18}[/tex] ( cross- multiply )
12 AB = 14 × 18 = 252 ( divide both sides by 12 )
AB = 21
Somebody please help
Answer:
IM FROM THE FUTURE :3
Step-by-step explanation:
the answer is -6 8-
i think 3:
Two trains leave a station going in opposite directions. The northbound train averages 87 miles per hour. The southbound train averages 113 miles per hour. How long will it take for the trains to be 600 miles apart?
Answer:
It takes 3 hours for the train to be 600 Miles apart
give the answer
the areaaaaaa
Answer:
16
Step-by-step explanation:
The figure shown is a trapezoid
Area of a trapezoid = 1/2(bottom base length + top base length) × height
Bottom base length = 7 units
Top base length = 1 unit
Height = 4 units
So area = 1/2 ( 7 + 1 ) × 4
==> add 7 and 1
Area = 1/2 (8) × 4
==> multiply 1/2 and 8
Area = 4 × 4
==> multiply 4 and 4
Area = 16
The group wants to travel from its current location on the map to the South Pole, and then directly back to the base camp. How many miles will they have to travel? Explain your answer.
Using the Pythagorean Theorem, it is found that the group will have to travel 90 miles.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem:
First, the group travels 5 x 5 = 25 miles to the south pole.Then, the distance to the camp is the hypotenuse of a right triangle with sides of 25 miles and of 12 x 5 = 60 miles, hence:[tex]d^2 = 25^2 + 60^2[/tex]
[tex]d = \sqrt{25^2 + 60^2}[/tex]
d = 65.
The total distance is given by:
Td = 25 + 65 = 90 miles.
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Maëlys veut installer une étagère à 60 cm du sol.
Pour vérifier que son installation est bien horizontale,
elle installe une corde à 30 cm au-dessus de l'étagère et
la tend jusqu'au sol afin d'être alignée avec le bord de
l'étagère. Elle arrive à 1,20 m du mur. La distance entre le
point d'attache et l'extrémité de l'étagère est de 50 cm.
l'installation de Maëlys est-elle bien horizontale ?
What is the slope of the line?
Answer:
[tex]-\frac{2}{3} x[/tex]
Step-by-step explanation:
Hey there!
To find slope, you take [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case
y2: 6
y1: 4
x2: -3
x1: 0
Now we plug in this information
[tex]\frac{6-4}{-3-0} \\\\\frac{2}{-3} \\\\-\frac{2}{3}[/tex]
Since this is the slope, you have to add a "x"
So, the slope is [tex]-\frac{2}{3} x[/tex]
A newly formed life insurance company has underwritten term policies on 120 women between the ages of forty and forty-four. Suppose that each woman has a 1/150 probability of dying during the next calendar year, and that each death requires the company to pay out $50,000 in benefits. Approximate the probability that the company will have to pay at least $150,000 in benefits next year
The probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
The probability of dying:
P(dying) = 1/150
P(living) = 1 - P(dying) = 1 - 1/150 = 140/150
There are 120 women.
P(x≥3) = 1 - [P(x=0) +P(x=1) + P(x=2)]
[tex]\rm P(x\geq 3)=1-[(120 \ choose \ 0)(1/150)^0)((149/150)^{120})+[/tex]
[tex]\rm (120 \ choose \ 1) ((1/150)^1) ((149/150)^{119}) +[/tex]
[tex]\rm (120 \ choose \ 2)((1/150)^2)((149/150)^{118})][/tex]
P(x≥3) = 0.047
Thus, the probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
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Exponential growth/decay problem 2
Answer:
a) decay
b) 2,950,000
c) 0.025
d) [tex]f(x)=2950000(0.975)^x[/tex]
e) 2,409,123
Step-by-step explanation:
Part (a)
Exponential DECAY, since the population was decreasing annually.
Part (b)
Initial amount = 2,950,000 people (in the year 2000)
Part (c)
Decay factor = 2.5% = 0.025 (in decimal form)
Part (d)
General form of exponential decay function:
[tex]f(x)=a(1-r)^x[/tex]
where:
a = initial amountr = rate of decay (in decimal form)x = time (in years)Given:
a = 2950000r = 0.025[tex]\implies f(x)=2950000(1-0.025)^x[/tex]
[tex]\implies f(x)=2950000(0.975)^x[/tex]
Part (e)
To determine the city's population in 2008:
[tex]x = 2008 - 2000 = 8[/tex]
[tex]\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}[/tex]
Find the value of x
Answer: 11
Step-by-step explanation:
the sum of six interior angles of a regular octagon is 800 the other two angles are equal find the size of each angle
An octagon is a polygon with 8 sides and angles. The two equal angles are 140 degrees each
How to calculate the sum of an interior angle of a polygon?An octagon is a polygon with 8 sides and angles
The formula for calculating the sum of interior angle of a regular polygon is expressed as:
S = (n-2) * 180
If the sum of six interior angles of a regular octagon is 800 the other two angles are equal, then;
800 + 2x = (8-2)*180
800 + 2x = 1080
2x = 1080 - 800
2x = 280
x = 140
The two equal angles are 140 degrees each
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Professor Mallory determines the distribution of students on five variables in her target population. She then uses nonprobability sampling to select students who fill the pre-established proportions of people in each combination of variables. Which sampling strategy did she use
The sampling strategy she use was a quota.
Quotas are meant to establish boundaries on the number of specific goods that are allowed to be lawfully imported into the country throughout a distinct period of time. In that, quotas are similar embargoes, except quotas don´t have explicit political purposes as embargoes do.
A Fixed quota would be a maximum amount not to be surpassed, while a tariff rate surcharge allows it, but with a higher duty.
What's the answer to this question? 4*(5t+1)/5
Answer:
[tex]\boxed{\sf{4t+\dfrac{4}{5} }}[/tex]Step-by-step explanation:
In order to solve this, you must use the distributive property.
[tex]\sf{\dfrac{4\left(5t+1\right)}{5}}[/tex]
Distributive property:
⇒ A(B+C)=AB+AC
⇒ 4(5t+1)
Multiply by expand.
4*5t=20t
4*1=4
Rewrite the problem down.
20t+4
20t+4/5
[tex]\text{FRACTION RULES: }\\\\\\\Longrightarrow: \sf{\dfrac{A\pm \:B}{C}=\dfrac{A}{C}\pm \dfrac{A}{C}}[/tex]
[tex]\Longrightarrow: \sf{\dfrac{20t+4}{5}=\dfrac{20t}{5}+\dfrac{4}{5}}[/tex]
You have to divide the numbers from left to right.
⇒ 20/5=4
[tex]\Longrightarrow: \boxed{\sf{4t+\dfrac{4}{5} }}[/tex]
Therefore, the correct answer is 4t+4/5.Answer:
[tex]4t + \frac{4}{5}[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]\frac{4(5t + 1)}{5}[/tex]
[tex]\frac{(4 * 5t) + (4 * 1)}{5}[/tex]
[tex]\frac{20t + 4}{5}[/tex]
Step 2: Isolate the numerator into two fractions
[tex]\frac{20t +4}{5}[/tex]
[tex]\frac{20t}{5} + \frac{4}{5}[/tex]
[tex]4t + \frac{4}{5}[/tex]
Answer: [tex]4t + \frac{4}{5}[/tex]
How would you solve this?
Answer:
the answer of the perimeter is B
Simply the expression.
4 (2m -6) - 3p - 2m + 8
Let's solve the equation.
4 (2m -6) - 3p - 2m + 8
= 8m - 24 - 3p - 2m + 8 (We simplified 4 (2m -6))
= 6m - 16 - 3p (We added the 8 to the 24)
= 6m - 3p - 16 (We organized the variables together so it matches an answer.)
The answer is A!
Answer: hii
The answer; 6m - 3p -16Step-by-step explanation:
How to solve your problem:
4 (2m -6) - 3p - 2m + 8
Simplify.
Distribute.
4 (2m -6) - 3p - 2m + 8
8m - 24 - 3p - 2m + 8
Add the numbers:
8m - 24 - 3p - 2m + 8
8m - 16 - 3p - 2m
Combine like terms:
8m - 16 - 3p - 2m
6m - 16 - 3p
Rearrange terms:
6m - 16 - 3p
6m - 3p - 16
Solution:
6m - 3p -16
Hopefully this helps you ~
- Matthew
HELpppppppppPPPPPPPPPPPPPPPpppppPPPPPPPP
Answer:
(a) mintutes, seconds
(b) Randomly pick 55 students to run a lap around the track and measure their times
Step-by-step explanation:
(a) When measuring distance like running you measure it in minutes and seconds
(b) When finding the average of a population you have to pick randomly and to get the best results you time them youself
Randomly pick 55 students to run a lap around the track and measure their times.
How many arrangements are there of the letters in the word "greet?"
342.5 divided by 34.25
The ratio of the measures if the sides of a triangle is 4:6:8, and its perimeter is 126 feet. What are the measures of the sides of the triangles
Answer:
56 feet.
Step-by-step explanation:
4k+6k+8k=18k=126⟹k=7
Therefore, the lengths are 4⋅7=28, 6⋅7=42 and 8⋅7=56 feet.
15 is 60% of what number?
25
hope it helps...!!!!
Melissa will paint a jewelry box that is in the shape of a cube. The surface area of the cube can be determined using the formula A = 682 wheres represents the side length the cube Determine the surface area of the box that Melissa will paint to the nearest tenth of a square inch if x = 2.
The surface area of the box that Melissa will paint is 24 square units
Surface are of a cubeA cube is a solid figure with 6 faces. The formula for calculating the surface area of the cube is expressed as:
A = 6L^2
where
L is the side length of the cube
Given
L = 2units
Substitute
A = 6(2)^2
A = 6 * 4
A = 24 square units
Hence the surface area of the box that Melissa will paint is 24 square units
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John, Britteny, Chloe, Kenji, Warner, and Juliette are in a race and are all considered equally fast what is the probability that John and Britteny would be the first two finishers
Detailed explanations are most welcome
Answer:
1/3
Step-by-step explanation:
There are 6 people partaking in this race.If John and Brittney are to be the first two finishers, then 2 out of the 6 people are the said first two finishers.That gives 2/6.By reducing the fraction, we have:(2÷2)/(6÷2) = 1/3.Hope this helps!
What is the factored form of this expression? x9-1000
A. (x3-10)(x3+10)(x2-10x+100)
B. (x3+10)(x6-10x3+100)
C. (x-10)(x+10)(x3-10x2+100)
D. (x3-10)(x6+10x3+100)
Answer:
D. (x^3 - 10)(x^2 + 10x^3 + 100).
Step-by-step explanation:
Using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2):
We have x^9-1000 :
- here a = x^3 and b = 10 so:
x^9-1000 = (x^3 - 10)(x^2 + 10x^3 + 100)
Sonja is spinning a spinner with 15 equal sectors labeled 1 through 15.
What is P(multiple of 6)?
2/15
4/15
2/5
3/5
Answer:
2/15
Step-by-step explanation:
there are only 2 numbers which are multiples of 6, which are both 6 and 12. That means it would be a 2/15 probability. You cannot simplify it more, so it will remain the same.
Answer:
2/15
Step-by-step explanation:
:)
The classroom has 20 students and
1
10
of the students have blonde hair. How many students have blonde hair?
Answer:
2 students out of 20 have blonde hair.
Step-by-step explanation:
20 was the total number if u divide 20 ÷ by 10 = 2
so 2 is 1/10
because is only 1 out of 10
Answer:
2 students.
Step-by-step explanation:
20 divided by 10 = 2
Dilation is enlarging or shrinking a figure by using a scale factor.
Using a scale factor bigger than one, creates a
figure.
Using a scale factor between 0 and
creates a
figure.
Create your own
dilation examples or find 2 images of dilation examples. Be
sure the two examples are different by showing one getting larger and one
getting smaller.
Answer:
Step-by-step explanation:
scale factor bigger than one, in math greater than, the figure is larger than the object being used a figure smaller than 1 creates a figure smaller than the original
Luckily you can just use your web browser to scale a screen up or down in it's scale. try it.. top right ellipse for go ogle chrome lets you scale over 100 per cent or 1 and also under 100 per cent or less than 1 remember 100 per cent = 1.00
The town of La Belle wants to build a soccer
field. They want it to be 50 yards wide and 80
yards long. What is the total area of the soccer
field? Show your process
Answer:
4000 yd^2
Step-by-step explanation:
50 yd * 80 yd = (50*80) ( yd * yd) = 4000 yd^2
Which relationships describe angles 1 and 2?
Select each correct answer.
vertical angles
adjacent angles
complementary angles
supplementary angles
2
Answer:
They are adjacent and supplementary
Step-by-step explanation:
Find the measure of angle A.
Angle 1. x+59
Angle 2. 84
Angle 3. x+51
I already know x= -7 But the measure of angle A is on the outside of the triangle
Ans: The measure of exterior angle i.e angle A is -52⁰.
You meant to say that the measure of an angle A is on exterior angle so let me elaborate it you clearly,
[tex]x + 59 \\ = - 7 + 59 \\= - 52[/tex]
Find the volume of the figure. Round answer to nearest hundredths place.
Answer: 540 nearest hundred is 500
Step-by-step explanation:
I multiplyed them together to get the answer.
Answer:
4834.9
Step-by-step explanation:
1) Split the Figure into a Cone and a Cylinder
2) Cylinder Formula V=πr²h And Cone V=1/3hπr²
3) π[tex]9^{2}[/tex]15 + 1/2(12)π([tex]9^{2}[/tex])
4) 3817.04+1017.88
5) 4834.9