Answer:
P(t) = 1000e^(0.01155)t
Step-by-step explanation:
Let the population of barangay be expressed according to the exponential formula;
P(t) = P0e^kt
P(t) is the population of the country after t years
P0 is the initial population
t is the time
If barangay has 1000 initially, this means that P0 = 1000
If the population doubles after 60years then;
at t = 60, P(t) = 2P0
Substitute into the formula
2P0 = P0e^k(60)
2 = e^60k
Apply ln to both sides
ln2 = lne^60k
ln2 = 60k
k = ln2/60
k = 0.01155
Substitute k = 0.01155 and P0 into the expression
P(t) = 1000e^(0.01155)t
Hence an exponential model for barangay's population is
P(t) = 1000e^(0.01155)t
What is an
equation of the line that passes through the points (-3,-7) and (8,-7)?
Answer: y = -7
graph attached.
Step-by-step explanation:
This is a horizontal line passing through -7 in the y-axis. It passes through all x-values
If 7 toothpaste tubes cost 40.50 how much does one tube cost?
Answer:5.78
Step-by-step explanation: It is 5.78 bc do 40.50 divided by 7 and you will get your answer
Brainliest please???
Answer:
Each tube costs about $5.79.
Step-by-step explanation:
To find the cost of each tube, divide the total cost by the total number of toothpaste tubes.
40.50/7 = 5.785714286 which approximates to 5.79
PLEASE HELP MEEE If there are 83 men and 17 women. What percentage of women are there
Answer: 17%
Step-by-step explanation: 83+17 = 100, 17/100 = 0.17 = 17%
The height of XYZ is the distance from the point Y to XZ find the area of the triangle round your answer to the nearest 10th if necessary HELPPP PLEASE
Answer:
Area of ΔXYZ = 10 square units
Step-by-step explanation:
Area of the triangle XYZ = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
Height of the triangle = AY
Base of the triangle = XZ
To get the length of any segment we will use the formula,
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2)}[/tex]
Here [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the segment.
Length of AY = Distance between (-1, 4) and (3, 6)
= [tex]\sqrt{(6-4)^2+(3+1)^2}[/tex]
= [tex]\sqrt{20}[/tex]
Length of XZ = [tex]\sqrt{(6-2)^2+(-2-0)^2}[/tex]
= [tex]\sqrt{20}[/tex]
Area of ΔXYZ = [tex]\frac{1}{2}(\sqrt{20})(\sqrt{20})[/tex]
= 10 square units
PLEASE HELP!! solve |2x-2| ≥6.
x ≤ -2 OR x ≥ 4
__________________________________________________________
Step-by-step explanation:We are given the inequality:
|2x - 2| ≥ 6
Getting rid of the Modulus:
Since 2x-2 is in modulus:
|2x-2| = -(2x-2) OR 2x-2
(since the modulus of both these values is 2x-2)
Hence, our inequality can be written in 2 different ways:
2x-2 ≥ 6 (if 2x-2 ≥ 1)-(2x - 2) ≥ 6 (if 2x-2 < 0)__________________________________________________________
Solving these 2 inequalities:
Solving inequality 1:
2x - 2 ≥ 6
2x ≥ 8 [adding 2 on both sides]
x ≥ 4 [dividing both the sides by 2]
This is the solution of the inequality if: 2x-2 ≥ 0
Solving Inequality 2:
-(2x-2) ≥ 6
It can be rewritten as:
2 - 2x ≥ 6
2 ≥ 6 + 2x [adding 2x on both the sides]
-4 ≥ 2x [Subtracting 6 from both sides]
x ≤ -2 [Dividing both sides by 2]
This is the solution of the given inequality if: 2x-2 < 0
__________________________________________________________
Solution of the given Inequality:
Therefore, the solution of the given inequality |2x-2| ≥ 6 are:
x ≥ 4 (if 2x-2 ≥ 0)
x ≤ -2 (if 2x-2 < 0)
Hence, option C is correct!
In RST, R = 23* and S = 136*. Which list has the sides of RST in order from shortest to longest?
RS, TR, ST
TR, ST, RS
ST, RS, TR
ST, TR, RS
TR, RS, ST
RS, ST, TR
Answer:
RS, ST, TRStep-by-step explanation:
The third angle measures:
T = 180° - (136° + 23°) = 21°Angles and opposite sides are:
S = 136° → TRR = 23° → STT = 21° → RSThe greater the angle, the greater the opposite side, therefore the sides in increasing order will be:
RS, ST, TRWhat is the domain of the square root function graphed below?
Answer:
The domain of the graph must be [tex]x\ge \:-4[/tex].
Therefore,
[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
Hence, option a is true.
Step-by-step explanation:
From the graph, it is clear that the graph is heading towards positive infinity from x=-4.
The point x=-4 is included in the graph as the starting point of the graph i.e. x=4 is showing a closed circle on x=4, and heading towards positive infinity onward.
i.e. [-4, ∞)
Hence, the domain of the graph must be [tex]x\ge \:-4[/tex].
Therefore,
[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
Hence, option a is true.
Work out (5 x 109)
109) x (9 x 10)
Give your answer in standard form.
Answer:
49050
Step-by-step explanation:
(5 x 109)x (9 x 10)
545×90
49050
So the answer is 49050
What is the perimeter of the rectangle 60ft and 50ft
Answer:
200 ft
Step-by-step explanation:
Answer:
220
Step-by-step explanation:
60 times 2 equals 120
50 times 2 equals 100
120 plus 100 equals 220
What is the probability that a randomly selected customer likes hot or iced coffee?
A.
B.
C.
D
Answer:
0.83
Step-by-step explanation:
add the hot, cold, and both sections together
xoxo, your highness...The probability of people liking hot or iced coffee is 0.61. Therefore, option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, according to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like cold coffee and 22% like both hot and iced coffee.
People like only hot coffee = 0.53
People like only iced coffee = 0.08
Customers like hot or iced coffee =0.53+0.08
= 0.61
Therefore, option C is the correct answer.
To learn more about the probability visit:
https://brainly.com/question/11234923.
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The graph of a function is shown: scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3 Which of the following correctly identifies the set of outputs? (4 points)
A. {−3, −2, 3}
B. {−1, 2, 3}
C. {(−3, 2), (−2, 1), (3, 3), (3, −1)}
D. {(2, −3), (1, −2), (3, 3), (−1, 3)}
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
i did flvs
Karen earns $5 by delivering newspapers each week. She saves $3 and she spends the rest. How many weeks will it take her to save enough money to buy a $35 gift card?
Answer:
give me 1hour
Step-by-step explanation:
Solve for X...........
Answer:
x = 60°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesGeometry
A box on an angle signifies a 90° angleAll angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set up equation
x° + 90° + 30° = 180°
Step 2: Solve for x
Combine like terms: x + 120 = 180Subtract 120 on both sides: x = 60°a company makes two different-sized ice cream cones. The smaller cones are 3.5 inches tall and have a diameter of 3 inches. The larger cones are 5.1 inches tall and have a diameter of 4.5. inches. About how much greater, to the nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone?
9514 1404 393
Answer:
18.8 cubic inches
Step-by-step explanation:
The formula for the volume of a cone is useful:
V = 1/3πr²h
Where r is half the diameter, we can use r=d/2 to write this in terms of diameter:
V = 1/3π(d/2)²h = (π/12)d²h
For the given dimensions, the volumes are ...
large cone: v = (π/12)(4.5 in)²(5.1 in) ≈ 27.04 in³
small cone: v = (π/12)(3 in)²(3.5 in) ≈ 8.25 in³
Then the difference in volume is ...
(27.04 -8.25) in³ ≈ 18.8 in³
The larger cone has about 18.8 cubic inches more volume.
solve for x.
√x + 20 = 9
possible answers:
17
61
81
101
Answer: 61
Step-by-step explanation:
[tex]\sqrt{x+20}=9\\\\x+20=81\\\\x=\boxed{61}[/tex]
The value of x will be 61.
What is mathematical expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mathematical expression is,
⇒ √x + 20 = 9
Now,
Solve the expression for the value of x as;
The mathematical expression is,
⇒ √x + 20 = 9
Take square on both side, we get;
⇒ (√x + 20 )² = 9²
⇒ x + 20 = 81
Subtract 20 both side, we get;
⇒ x + 20 - 20 = 81 - 20
⇒ x = 61
Therefore, The value of x will be 61.
Learn more about the mathematical expression visit:
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Answer each part. If necessary, round your answers to the nearest hundredth.
(a) Joe bought 13 pounds of rice for $7. How many pounds of rice did he get per dollar? pounds per dollar
(b) At Smith's Bike Rentals, it costs $29 to rent a bike for 6 hours. How many hours of bike use does a customer get per dollar? hours per dollar
Step-by-step explanation:
a) 13=$7
x=$1
(do cross multiplication)
13=7x
x=1.86 pounds
What is the product?
2 x [-1/0]
Answer:
=38
Step-by-step explanation:
Answer:
It's C [-2 0]
Step-by-step explanation:
If you multiply the product [-1 0] both by 2 you get [-2 0]
You buy butter for $3 a pound.
One portion of onion compote requires 1.7 oz of butter.
How much does the butter for one portion cost? Round to the nearest cent.
There are 16 ounces in one pound.
Set up a proportion and solve for x.
3/x = 16/1.7
16x = 3(1.7)
16x = 5.1
x = 5.1 ÷ 16
x = 0.31875
Rounding to the nearest cent, we get 30 cents.
A
rope
cut off?
is 3m long. If 25% is cut off, how many com was
25% of 3
Answer:
0.75meters
Step-by-step explanation:
25% of 3 is 0.75
Plz mark me brainliest
Anybody Know This. ? I Wanna Be Positive It’s C
Answer:.
Step-by-step explanation:
Answer:
The correct answer is A
Step-by-step explanation:
I think you are trying to find corresponding sides. In the answer that you think it is, it says BC = DF. Well, is you look triangle ABC you see that BC is at the bottom. However, this differs from triangle DEF because EF is the bottom line. So if you look at the answer A, you see that it has the correct corresponding sides. I hope that helps :))
PLZ HELP ASAP!!
If the parallel lines m and n are 6 units apart, how many units of translation is equivalent to the composition of two reflections over lines m and n?
9514 1404 393
Answer:
12 units
Step-by-step explanation:
Reflection over two lines x units apart is equivalent to a translation of 2x units. Since the given lines are 6 units apart, ...
the equivalent translation is of 12 units.
___
Example:
Lines at x=0 and x=6. Point (x, 0). After reflection over x=0, the point is located at (2·0 -(x), 0) = (-x, 0). After reflection of that over x=6, the point is located at (2·6 -(-x), 0) = (12 +x, 0). That is, 12 has been added to the x-coordinate, meaning the point was translated 12 units. (The translation is in the direction the second line is from the first.)
Find the range for the observations,5.6,7.1,8.3,3.7,6.8,4.1,8.4,2.7,4.4,8.2,2.8
Answer:
the range is 8-1=7
Step-by-step explanation:
HELP ME OUT HERE PLEASEEEEEEEEEEEEEEEEEEE
Answer:
5/8 quart
Step-by-step explanation:
Just take away 1/4 from 7/8Solve the equation. 3x + 2(4x − 6) = 8x + 1 What is the value for x? x =
Answer: x= 13/3
Step-by-step explanation: solve x
by simplifying both sides of the equation, then isolating the variable.
Answer:
[tex]x=\frac{13}{3}[/tex]
Step-by-step explanation:
The explanation on how to solve it is from the attached picture.
Hope this helps! :)
A person 6ft tall stands 10ft from point P directly beneath a lantern hanging 30 ft above the ground. The lantern start to fall, thus causing the person shadow to lengthen(L). Given that the lantern falls 16t2 feet in t seconds, how fast will the shadow be lengthening when t=1
Answer:
[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]
Step-by-step explanation:
In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).
From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:
[tex]\frac{L}{6}=\frac{10+L}{h}[/tex]
the height of the lamp can be found by subtracting the [tex]16t^{2}[/tex] distance the lamp falls in a given time t from the original 30ft the lamp was located at.
So the equation will now lok like this:
[tex]\frac{L}{6}=\frac{10+L}{30-16t^{2}}[/tex]
So now we can solve the equation for L, we can start by multiplying by the LCD SO WE GET:
[tex]L(30-16t^{2})=6(10+L)[/tex]
next, we can distribute the right side of the equation so we get:
[tex]L(30-16t^{2})=60+6L[/tex]
and subtract 6L from both sides so we get:
[tex]L(30-16t^{2})-6L=60[/tex]
and factor L, so we get:
[tex]L(30-16t^{2}-6)=60[/tex]
and solve for L:
[tex]L=\frac{60}{24-16t^{2}}[/tex]
now, we can differentiate this equation by using the chain rule, so we get:
[tex]dL=-\frac{60}{(24-16t^{2})^{2}}(-32t)dt[/tex]
which can be simplified to:
[tex]\frac{dL}{dt}=\frac{1920t}{(24-16t^{2})^{2}}[/tex]
and now we can substitute t for 1s so we get:
[tex]\frac{dL}{dt}=\frac{1920(1)}{(24-16(1)^{2})^{2}}[/tex]
[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]
PLEASEEEE HELP AND SHOW WORK WILL GIVE BRAINLIEST... LOVE Y'ALL!!! The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 5 hours at 950 km/h, how long would it take at 850 km/h?
Answer:
4 hour
Step-by-step explanation:
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane i.e.
[tex]t\propto v^2[/tex]
Here, t₁ = 5 h, v₁ = 950 km/h, v₂ = 850 km/h, t₂=?
[tex]\dfrac{t_1}{t_2}=\dfrac{v_1^2}{v_2^2}\\\\t_2=\dfrac{t_1v_2^2}{v_1^2}\\\\t_2=\dfrac{5\times (850)^2}{(950)^2}\\\\t_2=4\ h[/tex]
If the speed is 850 km/h then the time is 4 h.
You and your four friends have $25 to spend on snacks. A medium size popcorn costs $2.50 and a medium soft drink costs $1.50. Write and graph an inequality that represents the numbers of medium boxes of popcorn and medium soft drinks you can buy.
Answer:
Step-by-step explanation:
Step one:
given
Total money at hand=$25
cost of one popcorn=n $2.5
cost of drink= $1.5
total number of friends plus you= 4+1= 5
let the total amount spent be y
y= 5(2.5)+5(1.5)
y=12.5+7.5
y=20
The above shows that $20 is enough to cover the expenses, and there will be a balance of $5
What is -3/4 + 2 3/4
3 1/2
3 3/4
2 1/2
2
Answer:
2
Step-by-step explanation:
Answer:
Fourth Option
Step-by-step explanation:
In order to find the answer to this question you need to change the mixed number into a improper fraction and then add by finding the least common denominator (LCD).
[tex]-\frac{3}{4} +2\frac{3}{4}[/tex]
Convert into improper fraction:
[tex]2\frac{3}{4} =4\times2=8+3=11[/tex]
[tex]-\frac{3}{4} +\frac{11}{4}[/tex]
Since how the denominators are the same you can just add numerators:
[tex]-3+11=8[/tex]
[tex]=\frac{8}{4}[/tex]
Reduce:
[tex]8\div4=2[/tex]
[tex]4\div4=1[/tex]
[tex]=\frac{2}{1}[/tex]
[tex]\frac{2}{1} =2[/tex]
Hope this helps.
Pls help me figure out the slope
Answer:
[tex]m=\frac{-4}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (-3, 1)
Point (2, -3)
Step 2: Find slope m
Substitute: [tex]m=\frac{-3-1}{2+3}[/tex]Subtract/Add: [tex]m=\frac{-4}{5}[/tex]Pls help need to pass lesson
Answer:
Explanation below
Step-by-step explanation:
First Degree Equations
A first-degree equation can have one, none, or infinitely many solutions.
An equation like
2x + 3 = -x + 6
Has one solution: x=1
An equation like:
4x + 2 = 4x + 1
Has no solutions because when trying to solve for x we get:
2 = 1
This equality is false and no value of x can make it true
Finally, the equation:
3x + 2 = x + 2x + 2
Has infiniteyl many solutions, because when trying to solve it, we get:
2 = 2
Which is true regardless of the value of x
The first given equation:3x + 9 + 4x + x = ??
can be simplified as:
8x + 9 = ??
For this equation not having solutions, we should have 8x plus any number but 9 on the right side of the equation:
8x + 9 = 8x -3, or
8x + 9 = 8x + 4
The second given equation:3x + 9 + 4x + x = ??
can be simplified as:
8x + 9 = ??
If the equation has one solution, the only condition is that we should not have 8x on the right side. Thus any of those will do:
8x + 9 = 3x + 9
8x + 9 = -x + 5
8x + 9 = 0
The third equation:3x + 9 + 4x + x = ??
can be simplified as:
8x + 9 = ??
For this equation to have infinitely many solutions, the right side must be exactly equal to the left side:
8x + 9 = 8x + 9