Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
Learn more about exponential function here:https://brainly.com/question/2456547
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In a carnival game, players get 5 chances to throw a basketball through a hoop. If 7 out of 20 players made all 5 baskets, how many players out of 400 would you expect to make all 5 baskets?
=====================================================
Work Shown:
7/20 = 0.35 = 35% of the 20 players made all five baskets.
If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.
35% of 400 = 0.35*400 = 140
We expect about 140 people will make all five baskets.
Note how 140/400 = 0.35 = 35%
-------------
Through another alternative method, we can solve like this
7/20 = x/400
7*400 = 20*x ... cross multiply
2800 = 20x
20x = 2800
x = 2800/20 ... dividing both sides by 20
x = 140 which is the same result as before
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
On a coordinate plane, point A is (negative 3, 4) and point B is (4, 3).
Point B is the result of a 180° rotation.
Point A and B have the same x-coordinate.
Point B is the result of a 90° counterclockwise rotation.
Point A and point B are the same distance from the origin.
Answer:
D
Step-by-step explanation:
I took Edgy 2021 test
Answer:
D
Step-by-step explanation:
Uncle Frank has a paddock on his farm. The paddock is a right angled isosceles triangle and has area 16m2. What is the length of fence enclosing the paddock
Answer:
8 m
Step-by-step explanation:
Applying,
A = bh/2................ Equation 1
Where A = Area of the triangle, b = base of the triangle, h = height of the triangle.
Since the triangle is an isosceles triangle.
Then, b = h
Assuming, b = y m
Given: A = 16 m²
Substitute these values into equation 1
16 = (y×y)/2
16 = y²/2
y² = 16×2
y² = 32
y = √32
y = 4√2 m
Therefore,
b = 4√2 m and h = 4√2 m
Applying pythagoras theorem, to get the length of the fence enclosing the paddock
a² = b²+c²
a² = (4√2)²+(4√2)²
a² = 32+32
a² = 64
a = √64
a = 8 m
Hence the length of the fence enclosing the paddock is 8 m
PLZ HELP WILL GIVE BRAINLIEST IF RIGHT!!!
Christian goes out to lunch. The bill, before tax and tip, was $10.40. A sales tax of 6% was added on. Christian tipped 17% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:
$12.89
Step-by-step explanation:
value of tax:
6 : 100 = x : 10.40
x = (10.40 * 6)/100 = $0.624
new amount
10.40 + 0.624 = $11.02
value of tip
17 : 100 = x : 11.02
x = (11.02 * 17)/100 = $1.8734
Final amount
11.02 + 1.8734 = $12.89
f(x)=4 hallar el dominio, codominio, ceros o raices, vertices, asintotas, tabla de valores, graficas, identificar el tipo de funcion
Answer:
Tipo de función: Función Constante o Función Polinómica de Orden Cero
Dominio: [tex]Dom \{f(x)\} = \mathbb{R}[/tex]
Codominio: [tex]Ran \{f(x)\} = 4[/tex]
Asíntota: [tex]y = 4[/tex]
Raíces: No tiene.
Vértices: No tiene.
La tabla de valores y el gráfico se encuentran adjuntos al fondo.
Step-by-step explanation:
Sea [tex]f(x) = 4[/tex], el cual representa a una Función Constante o Función Polinómica de Orden Cero, cuyos dominio y codominio son [tex]Dom \{f(x)\} = \mathbb{R}[/tex] y [tex]Ran \{f(x)\} = 4[/tex]. No tiene vértices. Esta función tiene una asíntota horizontal coincidente con la función ([tex]y = 4[/tex]) y carece de raíces al ser [tex]f(x) \ne 0[/tex] para todo [tex]x\in \mathbb{R}[/tex].
Finalmente, agregamos una tabla de valores y la gráfica asociada a la función:
x -2 -1 0 1 2
y 4 4 4 4 4
If I have 75 oranges and I eat two and a half everyday for 30 days how many will I have eaten in one month
Answer:
all 75 of them
Step-by-step explanation:
2.5(30) = 75
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
A≈1075.21
d Diameter
37
d
r
r
r
d
d
C
A
Using the formulas
A=
π
r
2
d=
2
r
Solving forA
A=
1
4
π
d
2
=
1
4
π
37
2
≈
1075.21009
Step-by-step explanation:
Enter a range of values for x.
=============================================================
Explanation:
Ignore the sides that are 'a' units long.
We'll compare the sides that are 26 units and 27 units long. We see the 27 unit side is larger, which makes the 93 degree angle larger than the 3x-9 degree angle.
Symbolically, we would say
3x-9 < 93
At the same time, the 3x-9 is also larger than 0
So
3x-9 > 0 or 0 < 3x-9
Put together, we can form this compound inequality
0 < 3x-9 < 93
-------------------
Let's isolate x like so
0 < 3x-9 < 93
0+9 < 3x-9+9 < 93+9 .... add 9 to all sides
9 < 3x < 102
9/3 < 3x/3 < 102/3 .... divide all sides by 3
3 < x < 34
x is any number between 3 and 34, but cannot equal either endpoint
For example, x = 10 is valid since 3 < 10 < 34 is true. But x = 50 is not a solution since 3 < 50 < 34 is false. We can't have x = 3 and we also can't have x = 34 either, but we can have anything in between those endpoints.
Write an
explicit formula for An, the nth term of the sequence 5,-1, -7,....
Answer:
-6n + 11
Step-by-step explanation:
The difference between each number is 6 (-6)
If n=1 then -6n + 11 =5
If n=2 the (-6×2) + 11 = -1
If n=3 the (-6×3) + 11 = -7
and so on.
You use the difference between each number to identify how much you need to times n by the you use that information and figure out how much you need to add / subtract to find the first number in the sequence. To check you do the same thing for the second number or third number.
:]
What is the value of x
A. 100 B.50 C.25 D.35
Answer:
D
Step-by-step explanation:
I believe this is correct
Find the measurement of ∠PON
Given f(x) = 2x - 7 and g(x) = 3x + 2, find (fog)(x).
Answer:
(fog)(x)=6x-3
Step-by-step explanation:
In this problem, we are looking to find f of g of x. Simply put, we just have to plug g(x) into f(x). Whereever there is an x in f(x), we will replace with g(x).
[tex](fog)(x)= 2(g(x))-7\\(fog)(x)=2(3x+2)-7\\(fog)(x)=6x+4-7\\(fog)(x)=6x-3[/tex]
I hope this helps! Let me know if you have any questions :)
what is the y-intercept of this quadratic?
Answer:
The y-intercept is the value at which the graph of the function intersects the y-axis. Every quadratic has a (single) y-intercept. The reason for this is that the y-intercept is the function value at x = 0, and we can always substitute x = 0 into the quadratic.
ABCD and EFGH are rectangles with AB=10cm ,BC=7cm ,EF=7cm and FG =4cm ,all figures accurate to the nearest cm . Find the largest possible value of the shaded area . *
Answer:
42 cm^2
Step-by-step explanation:
Please find attached an image showing the diagram
area of shaded part = area of larger rectangle - area of smaller rectangle
Area of a rectangle = length x width
larger rectangle = 10 x 7 = 70 cm^2
smaller rectangle = 7 x 4 = 28cm^2
Area of shaded part : 70 - 28 = 42cm^2
need help with this problem
Answer:
2
Step-by-step explanation:
20%---4
20%---4
20%---4
15%---3
15%---3
10%---2
4-2=2
Answer:
2 scoops
Step-by-step explanation:
Hi there!
What the question tells us:
There were 20 sales in totalWe need to solve for the number of chocolate ice cream sales and the number of strawberry ice cream salesWe need to subtract: [# chocolate ice cream sales] - [# strawberry ice cream sales] = ?1) Determine the number of chocolate ice cream sales
The circle graph tells us that 20% of the scoops were for chocolate. To find the number of chocolate scoops, determine 20% of 20, which is the total number of scoops.
20 × 20%
Change 20% into a decimal
= 20 × 0.2
= 4
Therefore, the ice cream shop sold 4 scoops of chocolate ice cream.
2) Determine the number of strawberry ice cream sales
The circle graph also tells us that 10% of the scoops were for strawberry. To find the number of strawberry scoops, determine 10% of 20.
20 × 10%
Change 10% into a decimal
= 20 × 0.1
= 2
Therefore, the ice cream shop sold 2 scoops of strawberry ice cream.
3) How many more of these scoops were chocolate than strawberry?
[# chocolate ice cream sales] - [# strawberry ice cream sales] = ?
4 - 2 = ?
4 - 2 = 2
Therefore, 2 more of these scoops were chocolate than strawberry.
I hope this helps!
Congruent angle pairs : Find m
Answer:
75
Step-by-step explanation:
x+60 and 5x are vertical angles, which means they are equal
x+60 = 5x
Subtract x from each side
x+60-x = 5x-x
60 = 4x
Divide by 4
60/4 = 4x/4
15 =x
We want to find x+60
x+60
15+60
75
Answer:
∠GH = 75°
Step-by-step explanation:
x + 60° = 5x° ( vertical angles )
subtract x from both side
x - x + 60° = 5x - x
60° = 4x
divide each side by 4
60°/ 4 = 4x / 4
15 ° = x
To calculate, ∠GH
∠GH = x + 60 °
15 ° + 60° .. ( x = 15°)
= 75°
please help me im in need of serious help or ill flunk :(
Answer:
1. Interest: 15%
Amount owed: $500
2. Interest: 6%
Amount owed: $1,500
3. Interest: 18%
Amount owed: $12,500
4. Interest: 6%
amount owed: $5,000
Step-by-step explanation:
Quadrilateral ABCD is inscribed in a circle. If angle B measures 112°, what is the measure of angle D?
Answer:
68°
Step-by-step explanation:
If a quadrilateral is inscribed in a cirle, the sum of its opposite angles is 180°. Angles B and D are opposite => B+D=180° => D=180°-B=180°-112°=68°
Answer:
68°
Step-by-step explanation:
Since angles B and D are opposite each other, they are supplementary.
On a unit circle, the terminal point of 0 is (sqrt3/2,1/2)
What is 0?
Answer:
The measure of [tex]\theta[/tex] is 30°.
Step-by-step explanation:
In the statement, the angle has been misrepresented. The corrected statement is described below:
"On a unit circle, the terminal point of [tex]\theta[/tex] is [tex]\left(\frac{\sqrt{3}}{2}, \frac{1}{2} \right)[/tex]. What is [tex]\theta[/tex]?"
The measure of the angle ([tex]\theta[/tex]), in radians, is in standard form, that is, it is done with respect to the +x semiaxis. The measure of the angle whose terminal point is of the form [tex](x,y)[/tex] is determined by the following inverse trigonometric function:
[tex]\theta = \tan^{-1}\left(\frac{y}{x} \right)[/tex] (1)
If we know that [tex]x = \frac{\sqrt{3}}{2}[/tex] and [tex]y = \frac{1}{2}[/tex], then the measure of [tex]\theta[/tex] is:
[tex]\theta = \tan^{-1} \frac{\sqrt{3}}{3}[/tex]
[tex]\theta = 30^{\circ}[/tex]
The measure of [tex]\theta[/tex] is 30°.
Answer:
its 60 degrees
Step-by-step explanation:
a p e x 2021
Write a function for:
The output is 5 less than twice the input.
O y= 1/2x-5
y=5 - 2x
O y=2x - 5
O y= 5x - 2
Answer:
Step-by-step explanation:
Let us have y as the output and x as the input
5 is less than twice the input
twice the input is x * 2 = 2x
so we have 2x-5
Malloy solved the equation-5x-16=8 his work is shown below. Identity the error and where it was made. Step 1: -5x-16+16=8+16 Step 2: -5x=24 Step 3: -5x/5=24/5 Step 4: x=24/5
Answer:
he divided both sides by 5 instead of -5 in his last step
Step-by-step explanation:
Given the expression solved by max expressed as;
-5x - 16 = 8
Step 1: Add 16 to both sides
-5x - 16 + 16 = 8 + 16
-5x = 24
Step 2:
Divide both sides by -5
-5x/-5 = 24/-5
x = -24/5
According to Malloy calculation, he divided both sides by 5 instead of -5 in his last step
How many solutions are there to the system of equations graphed below if the lines are parallel?
Answer:
zero, or 0, or none. answer is A
Step-by-step explanation:
they never touch, just pick A
Answer:
0, the answer is a
Step-by-step explanation:
The perimeter formula for a rectangle is P=2L+2W. If the length of a rectangle is 2x^2+x-3 and the width is x+7, write an expression for the perimeter of the rectangle.
Answer:
P=(2x*2+x-3)L+ (x+7)2w
Step-by-step explanation:
Fill the table using function rule y=-3x+3
Answer:
Step-by-step explanation:
To solve this you just need to plug in your x values into the equations.
For example if x = 3,
when you plug it in you would get:
y = -3(3) + 3
y= -9 + 3
y = -6
You can plug in the rest of the x values and fill out your table.
You have entered a pie baking contest. In the contest, you must make several pies for the judges to taste. You will make your famous strawberry pie to compete with the other bakers. Utilize your skill with fraction to make correct calculations. You need to use 4/5 strawberries for a single pie, How many cups are needed for 2 pies?
Answer:
x=2.5 cups are needed for 2 pies
Step-by-step explanation:
4/5 or 0.8
Fraction form: 4/5x = 2 x= 5/4
Decimial form: 0.8x = 2 x = 2.5
Mixed number form: 2 1/2
Hope that helped :)
4-2(2x-3)-(2x-4)=-2(x+3)
Answer:
x = 5
Step-by-step explanation:
Given
4 - 2(2x - 3) - (2x - 4) = - 2(x + 3) ← distribute parenthesis on both sides
4 - 4x + 6 - 2x + 4 = - 2x - 6
- 6x + 14 = - 2x - 6 ( add 2x to both sides )
- 4x + 14 = - 6 ( subtract 14 from both sides )
- 4x = - 20 ( divide both sides by - 4 )
x = 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
Let's solve:
[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ [/tex]
Step 1: Simplify both sides of the equation.
[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ 4−2(2x−3)+−1(2x−4)=−2(x+3) \\ (Distribute the Negative Sign)
\\ 4+−2(2x−3)+−1(2x)+(−1)(−4)=−2(x+3) \\
4+−2(2x−3)+−2x+4=−2(x+3)
4+(−2)(2x)+(−2)(−3)+−2x+4=(−2)(x)+(−2)(3) \\ (Distribute) \\
4+−4x+6+−2x+4=−2x+−6 \\(−4x+−2x)+(4+6+4)=−2x−6(Combine Like Terms) \\ −6x+14=−2x−6
\\ −6x+14=−2x−6[/tex]
Step 2: Add 2x to both sides.
[tex]−6x+14+2x=−2x−6+2x \\ −4x+14=−6[/tex]
Step 3: Subtract 14 from both sides.
[tex]−4x+14−14=−6−14 \\ −4x=−20[/tex]
Step 4: Divide both sides by -4.
[tex] \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4} \\ x=5[/tex]
Jane bought 6 dozen banana at $250per dozen. She sells four and a half dozen at $35 each and the other were sold at $20 each. Determine if she made a profit or loss state her profit or loss as a percentage. Show working
Answer:
87.5% loss
Step-by-step explanation:
6 • 250 = 1500
4.5 • 35 = 157.5
6 - 4.5 = 1.5
1.5 • 20 = 30
157.5 + 30 = 187.5
1500x = 187.5
x = 0.125
12.5% is an 87.5% decrease
Ayuda con estos ejercicios Porfavor es para Mañana
David is six times older than Janet. If David is 48 years old, how old is Janet?
Answer:
janet would be 8 years old
Answer:
8
Step-by-step explanation:
Janet would be 8 cause yeah
Need urgent help for this math question will give brainliest
Answer:
1st box: 6x - 3 = 9
2nd box: 6x = 12
3rd box: x = 2
4th box: y = 4(2) - 3
5th box: y = 8 - 3
6th box: y = 5
Step-by-step explanation:
Part A-
1) 4x-3 = -2x+9
2) 4x+2x -3 = -2x+2x + 9
3) 6x -3 = 9
4) 6x -3+3 = 9+3
5) 6x = 12
6) 6x/6 = 12/6
7) x = 2
Part B-
1) y=4x-3
2) y=4(2)-3
3) y=8-3
4) y= 5
Therefore, x = 2 and y = 5.
I really hope this helps, good luck!