Given:
Population is 2005 = 35,700
growth rate = 4% = 0.04
To find:
The population in 2030.
Solution:
The general exponential growth model is
[tex]y=a(1+r)^t[/tex]
where, a is initial value, r is growth rate and t is time in years.
Let the initial year is 2005. So, number of years between 2005 to 2030 is
[tex]2030-2005=25[/tex]
Putting a=35,700, r=0.04 and t=25 in the above model.
[tex]y=35,700(1+0.04)^{25}[/tex]
[tex]y=35,700(1.04)^{25}[/tex]
[tex]y=35,700(2.665836)[/tex]
[tex]y=95170.3452[/tex]
Approximate the value to the nearest whole number.
[tex]y\approx 95,170[/tex]
Therefore, population of the district will be about 95,170.
Amount in 2030 is $95,169
Given that:
Amount invested = $35,700
Growth rate = 4% = 0.04
Time invested = 2030 - 2005
Time invested = 25 year
Find:
Amount in 2030
Computation:
A = P[1+r]ⁿ
Amount in 2030 = 35700[1+0.04]²⁵
Amount in 2030 = 35700[1.04]²⁵
Amount in 2030 = 35700[2.6658]
Amount in 2030 = $95,169
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If bc+ad=b solve for a
Answer:
a = (b - bc)/d
Answer:
ad=b-bc
a=b-bc/d or a=b-bc
--------
d
*everything is divided by d on the other side...so b-bc is all divided by d
What is the value of |7| + |-3|
Answer:
10
Step-by-step explanation:
7 + (-3) = -10
But it's |7| + |-3| which means it is the absolute value
So 10
Hope this helps :)
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Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.
A(-6, 9), B(2, 1); Ratio 5 to 3
Given:
Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1).
To find:
The coordinates of point P.
Solution:
Section formula: If a point divide a line segment in m:n, then the coordinates of point are
[tex]\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1). Using section formula, we get
[tex]P=\left(\dfrac{5(2)+3(-6)}{5+3},\dfrac{5(1)+3(9)}{5+3}\right)[/tex]
[tex]P=\left(\dfrac{10-18}{8},\dfrac{5+27}{8}\right)[/tex]
[tex]P=\left(\dfrac{-8}{8},\dfrac{32}{8}\right)[/tex]
[tex]P=\left(-1,4\right)[/tex]
Therefore, the coordinates of point P are (-1,4).
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long, about how far will the stake need to be from the middle of her tent?
A. 8.9 ft
B. 4 ft
C. 12 ft
D. 6.9 ft
Answer:
6.9 ft
Step-by-step explanation:
The Pythagorean Theorem. :)
a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
b^2 = 48
D = 6.928
<3 Enjoy,
Dea
The length of the stake needs to be from the middle of her tent will be 6.9 feet. Then the correct option is D.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long.
Then the length of the stake needs to be from the middle of her tent will be
We have
P = 4 ft
H = 8 ft
Then the base is given by the Pythagoras theorem.
B² = H² - P²
B² = 8² - 4²
B² = 64 - 16
B² = 48
B = 6.9 ft
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
Simon is selling candy bars for his class fundraiser. In each box of 56 candy bars, 18 are
peanut, and the rest are dark chocolate. Each dark chocolate candy bar costs $2.25.
If Simon raises a total of $117, selling a whole box, how much does each peanut candy bar
cost?
O $4.00
O $4.25
$2.00
$1.75
Nort
Answer:
it will be 1.75$
Step-by-step explanation:
56-18
38x2.25
117$ - 85.5$
31.5 / 18
Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer: C {48,65,80}
Step-by-step explanation:
In order for it to be a right triangle it would have to be {48,64,85}
Hope this helps
Given the polynomial 5x3−2x2+12, what is the leading coefficient?
******( I"LL GIVE YOU BRAINIEST)!!!******
A. -2
B. 3
C. 5
D. 12
Answer:
a.2
Step-by-step explanation:
Elevate the expression
(28-21) to the 2 power
Help!
Answer:
49
Step-by-step explanation:
28-21=7
7 to the power of two is the same as 7(7)
7(7)=49
The area of the September is 336cm is all this model rectangles are exactly the same what is the perimeter of rectangle if the length of one rectangle is 12 CM
Answer:
Perimeter is 80cm
Step-by-step explanation:
A rectangle's area is calculated by multiplying the length by the width. If we are given the area of the rectangle and the length then we would simply need to solve for the width of the rectangle using the area formula we just mentioned...
A = l * w
336[tex]cm^{2}[/tex] = 12cm * w ... divide both sides by 12cm
28cm = w
Now we can see that the width of this rectangle is 28cm. To find the perimeter we need to add all four sides together, since we know that a rectangle's opposite sides are the same then we add the length and the width twice to calculate the perimeter (P)
P = 12cm + 12cm + 28cm + 28cm
P = 80cm
Which is the greater fraction
3/4 or 11/16
Answer:
3/4
Step-by-step explanation:
3/4 = 75%
11/16 = about 68%
Therefore, 3/4 is greater
Which equations are correct?
Select each correct answer.
[tex]4c^4(3c^2)=12c^8[/tex]
[tex]3b^3(−2b^4)=−6b^12[/tex]
[tex]5y^4(2y^5)=10y^9[/tex]
[tex]5x^3(6x^4)=30x^7[/tex]
9514 1404 393
Answer:
C, D
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
__
The correct equations are the last two.
For the first two, the appropriate products are ...
[tex]4c^4(3c^2)=4\cdot3c^{4+2}=12c^6\\\\3b^3(a^2b^4)=3a^2b^{3+4}=3a^2b^7[/tex]
Write the equation in point-slope form of the line that contains the points (3,-5) and (5,- 1)
Answer:
y+5=2(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
The linear function passing through points (3,-5) and (5,- 1) is given by:
y = 2x+ 13.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
• The coefficient m is the slope of the function, representing the rate of change of the function.
• The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).
For this problem, the two points that form the function are given as follows:
(3,-5) and (5,- 1)
The slope is given by change in y divided by change in x, hence it is given by:
m = (y₂-y₁)/ (x₂-x₁)
m = (-1+5)/(5-3)
m = 4/2
m = 2
Then:
y = 2x + b.
When x = 3, y = -5, hence we can find the intercept b of the function as follows:
3 = 2 x -5 + b
b = 3+ 10
b = 13
Hence the equation is:
y = 2x+ 13
More can be learned about linear functions :
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what two numbers' sum=-4 and product=-2
Let a and b be the two numbers. Then
a + b = -4
a b = -2
Solve the second equation for b :
b = -2/a
Substitute this into the first equation:
a - 2/a = -4
Multiply both sides by a :
a² - 2 = -4a
Move 4a to the left side:
a² + 4a - 2 = 0
Use the quadratic formula to solve for a :
a = (-4 ± √(4² - 4(-2))) / 2
a = -2 ± √6
If a = -2 + √6, then
-2 + √6 + b = -4
b = -2 - √6
In the other case, we end up with the same numbers, but a and b are swapped.
What is the y intercept?
What is the slope?
Write the equation of the line to represent situation.
Answer:
y int is 20
slope = 2
equation: y = 2x + 20
The graph below relates y, the distance Kelly walked, to x, the amount of time that Kelly walked. What is the value of y when x = 1 ?
Answer:
You need to show the graph.
Step-by-step explanation:
please help me with this question
Answer:
12cm
Step-by-step explanation:
You can draw a triangle with hypotenusa 13, height h and base 5 (the difference between the radius 9 and 4). Then pythagoras tells us that
13² = h² + 5²
so
h = 13² - 5² = √144 = 12
A plumber charges a one-time fee of $75 plus a fixed hourly rate, h, in dollars. The plumber works at a customer's house for 2 hours and charges a total of $205.
What is the fixed hourly rate, in dollars, that the plumber charges?
Answer:
$65
Step-by-step explanation:
$205 - $75 = $130
$130 / 2 hours = $65
The hourly rate, in dollars, is $65 per hour.
In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC. Find BD if the perimeter of ABC is 50m and the perimeter of ABD is 40m
Given:
In isosceles triangle ABC, consider AB=BC and the segment BD with D a point on AC is the median to the base AC.
Perimeter of ABC is 50m and the perimeter of ABD is 40m.
To find:
The length of BD.
Solution:
In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC.
[tex]AB=BC[/tex] ...(i)
[tex]AD=CD[/tex]
[tex]AC=2AD[/tex] ...(ii)
Perimeter of ABC is 50m.
[tex]AB+BC+AC=50[/tex]
[tex]AB+AB+2AD=50[/tex] [Using (i) and (ii)]
[tex]2AB+2AD=50[/tex]
[tex]2(AB+AD)=50[/tex]
Divide both sides by 2.
[tex]AB+AD=25[/tex] ...(iii)
Now, perimeter of ABD is 40m.
[tex]AB+AD+BD=40[/tex]
[tex]25+BD=40[/tex] [Using (iii)]
[tex]BD=40-25[/tex]
[tex]BD=15[/tex]
Therefore, the length of BD is 15m.
Find the area of the trapezoid. Please help!
Answer:
Area = 1/2 (a + b )h
area = 1/2 ( 22.2 + 8.52 ) 9.86
area = 1/2 ( 30.72) 9.86
area = 1 x 30.72 x 9.86 ÷ 2
area = 151. 4496cm²
Answer:
The area of the trapezoid is 151.45cm sq
The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?
If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?
What is Simon’s total bill including tax and tip? What percent of the food bill is this?
Answer:
You are told tax is $3.40 which is 5% of the total priceWe want to find the original food bill not including the tax of $3.40We also want to find the tip quantity based on the original food billSo X * 0.05= 3.40 Gives us X= 68 Hence the original bill was $68Now $68* .20 = $13.6I'm confident you can answer the rest with the information I've provided.Simplify 81 to the negative 3 fourths power. (1 point)
Question 8 options:
1)
−27
2)
negative 1 over 27
3)
27
4)
1 over 27
Answer:
negative 1 over 27
Step-by-step explanation:
81 * negative 1 over 27 = -3
Answer:
[tex] \dfrac{1}{27} [/tex]
Step-by-step explanation:
[tex] 81^{-\frac{3}{4}} = [/tex]
[tex] = \dfrac{1}{81^{\frac{3}{4}}} [/tex]
[tex] = \dfrac{1}{(\sqrt[4]{81})^3} [/tex]
[tex] = \dfrac{1}{(3)^3} [/tex]
[tex] = \dfrac{1}{27} [/tex]
I need the top 2 pls
Answer:
Step-by-step explanation:
7:8 is 7/8
9:5
Find the next item in the pattern.
1, 10, 18, 25,...
30
28
38
31
PLS ANSWRR
Step-by-step explanation: It is gradually going up in numbers going down.
From 1 to 10 is 9
From 10 to 18 is 8
From 18 to 25 is 7
So from 25 to 31 is 6.
Hope this helps you! ;)
Answer:
31
Step-by-step explanation:
You add 9, then 8, and so on
Please Help!!!
(screenshot provided)
I have to find the value of X and Y in both questions. This is due today so please help ASAP!
Answer:
2. x=5
y=10
3. x=21
y=4
Step-by-step explanation:
2. 13y=20x+3y 10y=20x
8x+y=180-13y 14y=180-8x
y=2x plugging that into 14y=180-8x 28x=180-8x 36x=180 x=5
plug x into 10y=20x 10y=100 y=10
3. 3(x+y)=(4x-9) 3x+3y=4x-9 x=3y+9
5x=180-4x+9 9x=189 x=21
plug 21 into x=3y+9 21=3y+9 12=3y 4=y
PLEASE HELP WILL MARK BRAINLIEST
Answer:
A Plus Plumbing
Step-by-step explanation:
60(2)+80 = 120+80 = 200 < 250
Answer:
A- plus plumbing
Step-by-step explanation:
hope this helps
John wants to draw a circle graph showing his friends favorite ice cream flavors. When he polled his friends asking each their favorite flavor of ice cream, 35% of his friends aid chocolate, 20% of his friends said vanilla, 15% of his friends said Strawberry, 25% of his friends said mint chocolate chip, and 5% of his friends said flavors other than those previously listed. What will be the degree measure of the vanilla sector of the circle graph?
Answer:72
Step-by-step explanation:
which is a linear equation with a slope of 1/2 and a y-intercept of -5
Answer:
u say which but don't even give us options.
could somebody help please
The length of each side of an equilateral triangle is 74 mm, correct to the nearest millimetre.
Calculate the smallest possible perimeter of the triangle.
Answer:
222mm
Step-by-step explanation:
The perimeter of a triangle is the sum of all of the sides. This triangle is equilateral, which means that all sides are equal and in this case, each side is 74mm. So to find the perimeter of this triangle add each, 74+74+74, which equals 222. Therefore, the answer must be 222mm.
Answer:
the answer is 222 mm.
hope it works
There is 1/3 of a pie shared equally between 5 children. How much of the pie does each child receive?
1/9 pie
1/15 pie
1/18 pie
1/20 pie
Answer:
1/15 pie
Step-by-step explanation:
An easy way to do this is instead of dividing, multiply the denominator by 5. You get 15. You can say Im just making a coincidence, but try it yourself!
(1/3)/5 is basically multiplication. You may have heard the saying, "division with fractions is multiplication". Thats true. Turn 5 into 5/1 and multiply. 5/1x1/3.
you get 1/15. Hope it helps
Also you have to flip 5/1 to 1/5 and then multiply hehe. thats how you get 1/15
Answer:
Its B, 1/15 hope this helps
Step-by-step explanation: