If a population of 1000 people were to increae by 5% every year, what would the population be in 20 year?
The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.
How to estimate future population?
The future population can be estimated by the following equation:
P = P₀ × (1 + i)ⁿ
Where
P = population in the expected yearP₀ = current populationi = growth raten = number of periodsIf the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?
The population in the next 20 years would be
P = P₀ × (1 + i)ⁿ
P = 1000 × (1 + 0.05)²⁰
P = 1000 × (1.05)²⁰
P = 1000 × 2.6533
P = 2653 people
Hence, the population in the next 20 years would be 2653 people.
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In △abc, ​gf=17 in.​ what is the length of cf¯¯¯¯¯? enter your answer in the box. in.
The length of CF is 51 inches.
Complete question:
( In triangle ABC in which AD,BE and CF are the medians ),
In △ABC, GF=17 in. What is the length of CF¯¯¯¯¯? Enter your answer in the box.
What is the median in a triangle?
A line segment that joins a vertex to the mid-point of the side that is opposite to that vertex
The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...
CF = 3(GF) = 3(17 in)
CF = 51 in
So, the length of CF is 51 inches.
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the square base of a pyramid has an area of 144 square feet. If the slant height of the pyramid is 10 feet, what is the height of the pyramid
Answer: The answer would be 8ft
Step-by-step explanation:
A tram moved downward 35 meter in 7 econd at a contant rate. What wa the change in the tram' elevation each econd?
If a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
The total distance that tram moved downwards = 35 meters
Total time taken = 7 seconds
Here we have to use the unitary method
The change in the tram's elevation for each second = The total distance that tram moved downwards / Total time taken
Substitute the values in the equation
The change in the tram's elevation for each second = 35 /7
Divide the terms
= 5 meters
Hence, if a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
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please help me asap
According to the solving the co-ordinate mid-point D is (-4,0).
What is Mid-Point?A point on a line which bisects the same line is a mid point. It divides the line in two equal halves.
The mid-point is equidistant from both the ends of the given line.
Middle point formula in coordinate geometry
M={(x1+x2)/2,(y1+y2)/2}
According to the Given information:We need to find the coordinates of mid-point D of line AB, where
A is (-6x,4y)
B is (-2x,-4y)
By using Mid-point formula for coordinate D, we get
x=-6+(-2)/2
⇒ x=-6-2/2
⇒x=-8/2
⇒x=-4
And y coordinate
y=4+(-4)/2
⇒y=4-4/2
⇒y=0/2
⇒y=0
The coordinates of mid-point D of line AB is (-4,0)
Hence, D is (-4,0)
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Order the number from least to greatest.
0.8 8% 18% 1/8 8/20
Answer:
18%,1/8,18%, 8/20 0.8
Step-by-step explanation:
0.8 8/100 18/100 1/8 8/20
0.8 , 0.08 0.18 0.12 0.4
0.08 0.12 0.18 0.4 0.8
Answer:
8%, 1/8, 18%, 8/20
Step-by-step explanation:
Lets make all of these into decimals (its easier that way).
8% = 0.08
18% = 0.18
1/8 = 0.125
8/20 = 0.4
Now, put them into least to greatest! :)
3) Hugh has a goal of exercising 12/4 hours a day. He plans to go on several runs
today. His runs take him 4/6 of an hour. How many runs will Hugh need to go on?
At Berry Fun Farm, Liz picked 12 pints of berries. If 25% of the pints were blueberries, how many pints of blueberries did Liz pick?
Answer: 25% of 12 is 3
Step-by-step explanation:
Since there 25% is 1/4 of 100%, you'd need to divide.
There are 12 pints of berries.
If 1/2 of 25% is 6 since [tex]2 \sqrt{12}=6[/tex], you can say that the percentage would be 2/4.
Now, divide 12 by 4: [tex]4\sqrt{12}=3[/tex]
3 in this case would be the 1/4 and the 1/4 is substituting 25%
So there are 3 pints of blueberries.
PLEASE HELL!!
For the given item below, show your solution and tell whether lines m and n are parallel. If
not, state your reasoning
m/2 = (5x + 3), m/3 = (8x - 5)°, x = 14
As their measure of angles are not the same with respect to the positive x-axis they are not parallel.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know two lines are parallel if their slope is equal.
Given are two lines m and n.
For line m, slope(m) is m/2 = (5x + 3)° where x = 14.
Slope(m) is, m/2 = (5·14 + 3)°.
m/2 = 73°.
m = 146°.
For line n, slope(m) is, m/3 = (8x - 5)° where x = 14.
m/3 = 107°.
m = 321°.
As their measure of an angle is not the same with respect to the positive x-axis these two lines are not parallel.
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Find the value of x that would make the quadrilateral below a parallelogram.
The value of x=5 if given quadrilateral is parallelogram.
What is parallelogram?
A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. This means a parallelogram is a plane figure, a closed shape, and a quadrilateral.
We know, the opposite sides of parallelogram are equal
therefore, 5x-8 = 2x+7
5x -2x = 7+8
3x = 15
x =5
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40 POINTS (don't answer incorrectly just to get points)
The formula for the perimeter of a rectangle in terms of the width w is w=(P-2l)/2.
Given that, the formula for the perimeter of a rectangle is P=2(l+w).
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, the perimeter is P=2(l+w)
⇒ P=2l+2w
⇒ P-2l=2w
⇒ w=(P-2l)/2
Hence, the formula for the perimeter of a rectangle in terms of the width w is w=(P-2l)/2.
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True or false: If the ratio of QR to RS on the number line is 2:1, coordinate of R must be 2.
Step-by-step explanation:
false.
QR and ES are line segments.
a ratio between them is about their lengths, not about their position.
so, no, the given ratio has nothing to do with the coordinate itself.
please explain the answer
Answer: £4.26
Step-by-step explanation:
i think it is this:
the oranges cost £1.42 per kg and you have 1.5 kg of oranges so do £1.42 x 3=£4.26
A clerk is marking up merchandise 32%. The original price of an item is $450. What will be the retail price?
Answer:
$594
Step-by-step explanation:
450x1.32=$594
450+32%=$594
Let f(x) = 4x-8 and g(x)=x+3. Find f(g(x)) and g(f(x)).
f(g(x)) = (Simplify your answer.)
g(f(x)) =
(Simplify your answer.)
Answer:
[tex] \huge{ \bold{f(g(x)) = 4x + 4}} \\ \\ \huge{ \bold{g(f(x)) = 4x - 5}}[/tex]
Step-by-step explanation:
f(x) = 4x-8
g(x)=x+3
In order to find f(g(x)) you substitute g(x) into f(x) that's where ever you find x in f(x) you replace it with g(x) and solve
We have
[tex]f(g(x)) = 4(x + 3) - 8 \\ = 4x + 12 - 8 \\ = 4x + 4[/tex]
In order to find g(f(x)) you substitute f(x) into g(x) that's where ever you find x in g(x) you replace it with f(x) and solve
We have
[tex]g(f(x)) = (4x -8) + 3 \\ = 4x - 8 + 3 \\ = 4x - 5[/tex]
Hope this helps you
The polygon is enclosed by a circle, center o so that each vertex touches the circumference of the circle
show that the radius ao of the circle is 11.6 cm correct to the nearest 1 decimal place
Answer:
total is discarding 7 tables for you the Fall Festival by placing the same number of paper skeletons and bats on each table all together he used 84 scouters and 84 bats how many paper shapes went on each table
Write the equation of the line in slope-intercept form that passes through (3, 5) and is perpendicular to the line
3y + 4x = 12
Answer:
Step-by-step explanation:
find the gradient of given equation:
3y+4x=12
3y= -4x+12
y= -4/3x+4
gradient= -4/3
perpendicular gradient:
m1xm2=-1
-4/3m2=-1
-4m2=-3
m2= 3/4
find y-intercept by inputting coordinates in y=mx+c
5=3/4(3)+c
5=9/4+c
5-9/4=c
c= - 11/4
equation:
y=3/4x-11/4
the distribution of sample means approaches a normal curve as \ \ \ \ \ \ \ \ increases to infinity?
The correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'
In this question, we have been given a statement 'the distribution of sample means approaches a normal curve as _________ increases to infinity'
We need to complete the statement.
The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
This means, the distribution of sample means approaches a normal curve as the sample size i.e., n increases to infinity.
Therefore, the correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'
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Which equation represents the line that is
perpendicular to the graph of 4x + 3y = 9 and
passes through (-2, 3)?
A. 3x-4y=-18
B. 3x+4y=18
C. 3x-4y=-6
D. 3x+4y=6
The equation that represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is
[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
Let us revise some rules
1. The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]
2. The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y
The equation of the given line is 4x + 3y = 9
[tex]m = \frac{-a}{b}[/tex]
whereas a is the coefficient of x and b is the coefficient of y
Therefore the coefficient of x = 4 and the coefficient of y = 3
a = 4 and b = 3
[tex]m = \frac{-a}{b}[/tex]
The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]
That means reciprocal the fraction and change its sign
The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]
The form of the equation is y = mx + b
- Substitute m by [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex] x + b
To find b substitute x and y in the equation by the coordinates
of a point on the line
The perpendicular line passes through point (-2 , 3)
x = -2 and y = 3
3 = [tex]\frac{3}{4}[/tex](-2) + b
3 = [tex]\frac{-3}{2}[/tex]+ b
Add to both sides
[tex]\frac{9}{2}[/tex] = b
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
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115% = 38x + 161y
What is 100%?
Answer:
100% is 32.3x + 136.85y------------------------
Given115% = 38x + 161yFind 100%100% = 115% - 15% (38x + 161y) - 15% = (38x + 161y)*(1 - 0.15) = (38x + 161y)*0.85 =38x*0.85 + 161y*0.85 = 32.3x + 136.85yAnswer:
32.3x + 136.85y
Step-by-step explanation:
Let's take it as,
→ z = 100%
Forming the equation,
→ z + 15% = 38x + 161y
Now the value of z will be,
→ z + 15% = 38x + 161y
→ z = 38x + 161y - (1 - (15/100))
→ z = (38x + 161y) × (1 - 0.15)
→ z = (38x + 161y) × (0.85)
→ [ z = 32.3x + 136.85y ]
Hence, the answer is above.
The area of a parallelogram is 12 square units. one side of the parallelogram is 18 units long. the other side is 6 units long. determine whether each dimension could be the height of the parallelogram. pick all correct. a. 2/3 units b. 3/2 units c. 2 units d. 3 units
option (a) and (C).
The height of the parallelogram is 2 units and 2/3 units.
The sides of parallelogram are 6 units and 18 units .
Area of parallelogram (A) =12 square units.
Base of parallelogram (B) = 6 units.
formula used:
A = B*H
12 = 6*H
H = 12/6
H = 2 units.
if, base of parallelogram (B) = 18 units
A = B*H
12= 18*H
H = 12/18
H = 2/3 units.
the height of parallelogram are 2 and 2/3 units.
#123
For more information:
The parallelogram has a height of 2/3 units.
Given that,
A parallelogram has a surface area of 12 square units. The parallelogram has a side that is 18 units long. There are 6 units on the other side.
For a parallelogram to find the height;
Let,
Area of the parallelogram = Base * Height
12 = 18 * H
H = 12/18
H = 2/3
Therefore, the height of the parallelogram is 2/3 units.
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help me the pic is the queston
What is the average of 1 to 9 numbers?.
The average of 1 to 9 Integers is 5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.
By average, do you mean overall?By dividing the total number of values by the total number of numbers, the average can be computed. A mean is the mathematical average of a set of two or more data items. Common names for average include mean and mathematical mean. The term "mean" simply represents the average of the sample.
What do you mean by average?The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the amount of units in the list. The term "mean" in statistics also refers to the average of a particular set of numerical data.
To calculate average = 1+2+3+4+5+6+7+8+9/9
=45/9= 5
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A toy company makes wooden blocks. A carton holds 87 blocks.
How many blocks can 15 cartons hold?
The cartons can hold
blocks.
Using mathematical operations, we know that 15 cartons can hold 1,305 wooden blocks.
What exactly are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands as well as a math operator. The provided operands or integers must adhere to a predetermined body of norms relating to the math operator's symbol. The order of operations is a rule that specifies the right steps to take when analyzing a mathematical equation. The PEMDAS operations you can recollect in this sequence are parentheses, exponents, multiplying, division (from Left to Right), addition, and subtraction (from left to right).So, a number of blocks 15 cartons can hold:
We know that,
1 carton can hold 87 blocks.Now, calculate as follows:
15 cartons = 87 × 1515 cartons = 1,305 blocksTherefore, using mathematical operations, we know that 15 cartons can hold 1,305 wooden blocks.
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find the measure of the indicated angle, GIVE STEPS PLEASE!!
The measures of the indicated angles are 35 °, 238.73° & 18.40 ° respectively.
What are the trigonometric identities?
All trigonometric identities are based on the six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent are the values. All of these trigonometric ratios are defined using the sides of a right triangle, such as an adjacent side, opposite side, and hypotenuse side.
Let's consider,
x = opposite side of an angle of the triangle.
y = adjustant side of an angle of the triangle.
z = hypotenuse of the triangle.
θ = angle of the triangle.
i) In the first diagram
We have,
y = 49
z = 60
[tex]cos\theta = \frac{y}{z}[/tex]
θ = cos⁻¹(0.816)
θ = 35 °
ii) In the second diagram
We have,
y = 41
x = 10
θ = ?
[tex]tan\theta = \frac{x}{y}[/tex]
θ = tan⁻¹(0.2439)
θ = 238.73°
i) In the third diagram
y = 53
x = 17
θ = ?
[tex]tan\theta = \frac{x}{y}[/tex]
θ = tan⁻¹(3.11)
θ = 18.40 °
Hence, the measures of the indicated angles are 35 °, 238.73° & 18.40 ° respectively.
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Last year, Jacky's age was six times the age of his son. If Jacky's son was 5 years old last year, find the age of Jacky this year.
what equations could i use with 1 2 3 4 5 to get 35
Answer:
(5x5) + (5x2)
Step-by-step explanation:
is that helpful i dont really get what youre asking
Answer:
1+2*3*5+4
Step-by-step explanation:
Help me pls.
100 points for those who work it out
Both areas are equal, 4 cm²
Answer:
Area of triangle = 4 cm²
Area of square = 4 cm²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
From inspection of the given diagram:
b = 2 cmh = 4 cmSubstitute the values into the formula to find the area of the triangle:
[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \times 2 \times 4\\A&=1 \times 4\\A&=4\;\sf cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
From inspection of the given diagram:
s = 2 cmSubstitute the value into the formula to find the area of the square:
[tex]\begin{aligned}\implies A&=2^2\\A&=2 \times 2\\A&=4\;\sf cm^2\end{aligned}[/tex]
The area of the triangle is 4 cm², and the area of the square is 4 cm², thus proving that the triangle and the square have the same area.
About 75% of the wate produced in the U. S i recyclable. Micah’ family ha 40 pound of trah. He want to etimate how much of thi trah i recyclable
Answer:
30 lb
Step-by-step explanation:
75% of trash is recyclable.
40 lb trash.
75% of 40 lb = = 40/100 × 75 lb = 0.40 × 75 lb = 30 lb
Answer: 30 lb
a rock is thrown off a 200-foot cliff. the trajectory of the rock is modeled by the function h(t)=(-10t^2)+200, where h is the height in feet and t is the time in seconds. when will the rock hit the ground.
Answer:
4.47 seconds.
Step-by-step explanation:
Given function:
[tex]h(t)=-10t^2+200[/tex]
where:
h is the height (in feet).t is the time (in seconds).The rock will hit the ground when h(t) = 0.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm\sqrt{20}\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}[/tex]
As time is positive, t = 4.47 s only.
