Using the exponential growth formula, the town's population of 14,000 growing at a rate of 5% per year will reach 27,706 after 14 years.
To calculate the future population of a town with a given growth rate, we use the formula for exponential growth, which is:
[tex]P_{t} = P_0 (1 + r)^t[/tex]
Given a town with an initial population (P0) of 14,000 and a growth rate (r) of 5% or 0.05, want to find the population after 14 years (t).
Plugging in the values into the formula:
P(14) = 14,000 × (1 + 0.05)¹⁴
P(14) = 14,000 (1.05)¹⁴
P(14) = 14,000 1.9791
P(14) = 27,706.24
To the nearest whole number, the population after 14 years will be 27,706.
The graph f(x) shown below resembles the graph of g(x)=x3 but it has changed somewhat. Which of the following could be the equation of f(x)?
Answer: C
Step-by-step explanation:
The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.
Answer: 1.5 common difference
Step-by-step explanation:
7 = 10.2, 12 = 17.7
d = 17.7 - 10.2/ 12 - 7
d = 7.5/ 5
d = 1.5
Identify the polygon that has vertices P(−6,2), A(−3,3), T(0,2), and H(−3,1), and then find the perimeter and area of the polygon.
rhombus; P=6 units; A=4√ 1 0 units2
parallelogram; P=6 units; A=4√ 10 units2
rhombus; P=4√ 10√ units; A=6 units2
rhombus; P = 40 units; A = 12 units2
Answer:
[tex]p=4\sqrt{10}units[/tex]
[tex]A=6units[/tex] [tex]square[/tex]
Step-by-step explanation:
Given,
[tex]P\left ( -6,2 \right ),A\left ( -3,3 \right ),T\left ( 0,2 \right ),H\left ( -3,1 \right )[/tex]
Distance between two points
[tex]h=\sqrt{\left ( x_{1}-x_{2} \right )^{2}+\left ( y_{1} -y_{2}\right )^{2}}[/tex]
[tex]PA=\sqrt{\left ( -6+3 \right )^{2}+\left ( 2-3 \right )^{2}}[/tex]
[tex]=\sqrt{9+1}=\sqrt{10}units[/tex]
[tex]AT=\sqrt{\left ( -3+0 \right )^{2}+\left ( 3-2 \right )^{2}}[/tex]
[tex]=\sqrt{9+1}=\sqrt{10}units[/tex]
[tex]TH=\sqrt{\left ( 0+3 \right )^{2}+\left ( 2-1 \right )^{2}}[/tex]
[tex]=\sqrt{9+1}=\sqrt{10}units[/tex]
[tex]HP=\sqrt{\left ( -3+6 \right )^{2}+\left ( 1-2 \right )^{2}}[/tex]
[tex]=\sqrt{9+1}=\sqrt{10}units[/tex]
[tex]PA=AT=TH=HP[/tex] (i)
Length of diagonal
[tex]d_{1} =PT=\sqrt{\left ( -6+0 \right )^{2}+\left ( 2-2 \right )^{2}}[/tex]
[tex]=\sqrt{36+0}=6[/tex]
[tex]d_{2}=AH=\sqrt{\left ( -3+3 \right )^{2}+\left ( 3-1 \right )^{2}}[/tex]
[tex]=\sqrt{0+4}=2units[/tex]
Length of diagonals are not equal
[tex]d_{1} \neq d_{2}[/tex] (ii)
From above conditions this polygon is rhombus
Perimeter of rhombus =4×length of side
[tex]p=4\sqrt{10}units[/tex]
Area of rhombus
[tex]A=1/2\times d_{1}\times d_{2}[/tex]
[tex]a=1/2\times 6\times 2[/tex]
[tex]A=6units[/tex] [tex]square[/tex]
To answer the student's question, the identification of a polygon and its perimeter and area calculation depend on analyzing the given vertices, using the distance formula to calculate the perimeter, and appropriate area formulas related to the specific polygon identified.
Explanation:The student is asking about the identification of a polygon with four given vertices and the calculation of its perimeter and area. To identify the polygon, we need to analyze the given points P(−6,2), A(−3,3), T(0,2), and H(−3,1). By plotting these points and connecting them, we could determine the shape and properties of the polygon.
Once the polygon is identified, we can calculate the perimeter by finding the distance between each pair of consecutive vertices (sides of the polygon) and summing them up. The area can be found using the appropriate formula, which is dependent on the type of polygon we identify.
Without the explicit calculations included in the student's question, it is difficult to verify the exact answer among the choices presented. However, we can guide them to use the distance formula for the perimeter and, depending on the shape, utilize formulas such as for a rhombus or parallelogram to find the area. For example, the area of a parallelogram is the base times height, and for a rhombus, it can also be calculated as half the product of its diagonals.
What is a slope that is parallel to a slope of 5/3
Answer: 5/3
Step-by-step explanation: Parallel lines have the same slope.
So, a parallel slope would be 5/3
Hope this helped!
You start at (-5, 5). You move down 6 units and up 5 units. Where do you end?
Answer:
(-5, 4)
Step-by-step explanation:
if you are moving up and down only the y part of the coordinate will change so 5 going 6 down would put you at -1 then going 5 up would put you at 4
Final answer:
Starting at (-5, 5), moving down 6 units and then up 5 units results in a final position of (-5, 4).
Explanation:
If you start at the point (-5, 5) and then move down 6 units, your vertical position decreases by 6. That means you subtract 6 from 5, the y-coordinate, resulting in -1. However, if you then move up 5 units, you're adding 5 back to your y-coordinate. So, you take -1 and add 5, which results in 4. Your final position then is still at the same x-coordinate, -5, but with a new y-coordinate of 4. Therefore, the point you end up at is (-5, 4).
Great a word problem for x+2=3x-8
Answer:
x plus 2 equals three x minus eight.
What is the quadratic equation with the given roots 3 and -2/3
Answer:
x^2 - 7/3x-2
Step-by-step explanation:
x1=3, x2 =-2/3
(x-x1)(x-x2)=(x-3)(x-(-2/3))=
(x-3)(x+2/3)=x*x+x*2/3-3*x-3*2/3=
x^2 +2/3x-3x-6/3=
x^2 +2/3x-9/3x-2=
x^2 - 7/3x-2
Show it four ways
15+18=33
Answer:
Check Explanation
Step-by-step explanation:
15 cars plus 18 cars is 33 cars
15 fish plus 18 fish is 33 fish
15 cups plus 18 cups is 33 cups
15 dollars plus 18 dollars is 33 dollars
A farmer owns a rectangular-shaped farm. She knows that the length is 2 km longer than the width and the perimeter is 16 km. Find 'x', the width of her
farm.
Answer:
x = 3
Step-by-step explanation:
x + x + x + 2 + x + 2 = 16 (combine like terms)
4x + 4 = 16 (subtract 4 from each side)
4x = 12 (divide each side by 4)
x = 3
Let's check:
(3 + 2) × 2 = 10
3 × 2 = 6
10 + 6 = 16
It works.
Answer:
length= 5 km
Width=3 km
Step-by-step explanation:
Length=Width+2
L=W+2
Perimeter = 16 km
Perimeter of the rectangular field = 2(Length+Width)
[tex]16 = 2*(Width+2+Width)\\\16=2(W+2+W)\\\\16=2(2W+2)\\\\16/2=2W+2\\\\8=2W+2\\\\2W=8-2\\\\2W=6\\\\W=6/2\\\\W=3 km[/tex]
Length(L)=Width+2= 3+2=5 km
length= 5 km
Width=3 km
Select the decimal that is equivalent to 13^75
Answer:
3.51359276e83
Step-by-step explanation:
3.51359276e83
A college has a 2:3 ratio from men to women what fraction of the college is women
[tex]\frac{3}{5}[/tex] of the fraction of the college is women
Explanation:
The college has a 2:3 ratio from men to women.
The number of men in the college is 2.
The number of women in the college is 3.
The total number of students in the college is [tex]2+3=5[/tex]
We need to determine the fraction of the college is women.
The fraction of the college can be determined by substituting the values in the formula,
[tex]\frac{\text { Number of women }}{\text { Total number of students }}$[/tex]
Substituting the values, we have,
[tex]\frac{3}{5}[/tex]
Hence, [tex]\frac{3}{5}[/tex] of the fraction of the college is women.
There are 40 students playing dodge ball in a high school gym that is 100 feet long by 60 feet wide. There are 12,000 balls available in the gym to throw. What is the population density of the balls in the gym (balls per square foot)?
Answer:
2 balls/ft²
Step-by-step explanation:
The area of the gym is:
A = (100 ft) (60 ft)
A = 6,000 ft²
The population density is:
D = 12,000 balls / 6,000 ft²
D = 2 balls/ft²
Final answer:
To calculate the population density of balls in a gym, divide the total number of balls by the gym's area in square feet. In this case, with 12,000 balls and a gym of 6,000 square feet, the population density is 2 balls per square foot.
Explanation:
The question involves calculating the population density of balls in a gym. First, we need to find the area of the gym to understand the space these balls will occupy. The gym is 100 feet long and 60 feet wide, thus its area is 100 * 60 = 6,000 square feet.
Next, we're told there are 12,000 balls available in the gym. To find the population density of the balls, the number of balls is divided by the area of the gym. So, the population density is 12,000 balls divided by 6,000 square feet, which equals 2 balls per square foot.
Write this ratio as a fraction in simplest form without any units. 21 feet to 10 yards
The ratio 21 feet to 10 yards can be simplified and written as a fraction. By converting feet to yards, we get the ratio 7 yards to 10 yards or the fraction 7/10, which is already in its simplest form.
Explanation:In order to write the ratio 21 feet to 10 yards as a fraction in simplest form, we need to first convert feet into yards. One yard is equivalent to three feet. Therefore, we can transform 21 feet to 7 yards. The ratio thus translates to 7 yards to 10 yards. Writing this ratio as a fraction, we get 7/10. Since 7 and 10 have no common factors other than 1, the fraction 7/10 is already in its simplest form.
Learn more about Ratios and Fractions here:https://brainly.com/question/35908115
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rewrite 2y = -1x - 8 in y = mx + b form. SHOW STEPS
Answer:
y = [tex]-\frac{1}{2} x[/tex] - 4
Step-by-step explanation:
Simply divide both sides by 2.
2y = -1x - 8
[tex]\frac{2y}{2} =\frac{-1x-8}{2}[/tex]
y = [tex]-\frac{1}{2}x - \frac{8}{2}[/tex]
y = [tex]-\frac{1}{2} x[/tex] - 4
Answer:y=-x/2 - 4
Check the picture for explanation
Step-by-step explanation:
Susan has 6 apples.
She split the 6 apples
With her and 2 of her friends.
How many apples does each person get?
PLEASE MARK BRAINLIEST!
Answer:
Lets see...
Step-by-step explanation:
Facts:
she has 6 applesShe has to divide them among her and her friends evenlyIf she has to divide them among her and her 2 friends, that means that she has to divide 6 apples among 3 people.So the real question is, "If you have 6 apples and 3 people to give them to, how many apples will each person get?"
Solve:
6 ÷ 3 = 2
Each person will get 2 apples.
I hope this helps!
- sincerelynini
solve the following system of equations 2x-5y=6 and -2x+10y=-16
Answer:
The answer is
y=-2
x=-2
Step-by-step explanation:
You use combination to solve it;
2x-5y=6 minus 2x+10y=-16
5y=-10
y=-2
x=-2
plug in the solution into the equation to verify your answer
please help me I really need to finish this asap!!
7.5 for question 9
The angle one is 44 + 4x =180
16 for question 13
30 for question 15
Question 13 pls. Brainliest for the first answer
Answer: a child ticket costs $14.50
Step-by-step explanation:
x=children ticket
x+4.50=adult ticket
3 children and 2 adult
3x+2(x+4.50)=81.50
3x+2x+9.00=81.50
5x+9.00=81.50
5x+9.00-9.00=81.50-9.00
5x=72.50
5x/5=72.50/5
x=14.50
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees. What is the measure of Angle A B C ? 36° 43° 72° 144°
Answer:
The measure of angle ABC is 36° ⇒ 1st answer
Step-by-step explanation:
Let us revise some important facts in the circle
The measure of the center angle is equal to the measure of its subtended arcThe measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arcThe vertex of a central angle is the center of the circle and its sides are radii in the circleThe vertex of an inscribed angle is a point on the circle, and its sides are chords in the circleIn circle D
∵ D is the center of the circle
∵ A and C lie on the circle
- DA and DC are radii
∴ ∠ADC is a central angle subtended by arc AC
∴ m∠ADC = m of arc AC
∵ m∠ADC = (7x + 2)°
∵ m of arc AC = (8x - 8)°
- Equate them to find x
∴ 8x - 8 = 7x + 2
- subtract 7x from both sides
∴ x - 8 = 2
- Add 8 to both sides
∴ x = 10
Substitute the value of x in the measure of ∠ADC
∵ m∠ADC = 7(10) + 2 = 70 + 2
∴ m∠ADC = 72°
∵ AB and BC are two chords in circle D
∴ ∠ABC is an inscribed angle subtended by arc AC
∵ ∠ADC is a central angle subtended by arc AC
- By using the 2nd fact above
∴ m∠ABC = [tex]\frac{1}{2}[/tex] m∠ADC
∴ m∠ABC = [tex]\frac{1}{2}[/tex] × 72
∴ m∠ABC = 36°
Answer:
36
Step-by-step explanation:
Evaluate this function: For f(x) = -2x + 9, find f(5)
f(5) is -1
Step-by-step explanation:
Step 1: Given f(x) = -2x + 9, find f(5)f(5) = -2 × 5 + 9 = -10 + 9 = -1
Answer:
The answer is -1
Step-by-step explanation:
F(x)=-2x+9
When x=5
Substitute x=5 in the above equation
F(5)=-2(5)+9
F(5)=-10+9
F(5)=-1
A rational expression simplifies to1/2 The denominator of the original expression is given. Which polynomial is the numerator?
?/6x2 - 2x - 8
6x2 – 2x – 16
3x - 4
12x2 - 4x – 16
o 3x2-x-4
Answer:
3x^2-x-4
Step-by-step explanation:
Answer:
The correct answer is D.
Step-by-step explanation: Edge 2021.
If f(x) = 4x^0 + (4x)^-1, what is the value of f(4)
Answer:
[tex]\frac{65}{16}[/tex] or 4.0625
Step-by-step explanation:
To solve this problem, all we have to do is input the value x = 4 into the equation and solve.
f(4) = 4(4)^0 + (4x)^-1
f(4) = 4(1) + 1/4(4)
f(4) = 4 + 1/16
f(4) = [tex]\frac{64}{16}[/tex] + [tex]\frac{1}{16}[/tex]
f(4) = [tex]\frac{65}{16}[/tex]
f(4) = 4.0625
How many solutions does the system of linear equations represented in the graph below have?
A: No solution
B: one solution
C: infinitely many solutions
D: none of the above
Answer:
infinite solutions
Step-by-step explanation:
If your graph has lines that are not touching and are parallel to each other, there would be an infinite amount of solutions to this graph.
The number of solutions should be infinite solutions
The following information should be considered:
In the case when the graph contains lines that are not touching and are parallel to each other, so there should be infinite amount of solutions to this graph. Therefore, the option c is correct.learn more: https://brainly.com/question/13981855?referrer=searchResults
Divide. Round your answer to nearest hundredth. 0.391 ÷ 0.48
Answer:0.81
Step-by-step explanation:
0.391/0.48 =0.814583333...
So when rounding up to the nearest hundredth you have to stop 0.81 and because 4 is the next number after 0.81, you don't need to change the 1 at the end.
A car travels 20 1/2 miles in 2/3 of an hour. What is the average speed, in miles per hour, of thr car?
Average speed of the car is 29.85 miles/hr
Step-by-step explanation:
Step 1: Calculate speed when distance = 20 1/2 = 20.5 miles and time = 2/3 hr = 0.67 hrs.Speed = Distance/Time = 20.5/0.67 = 29.85 miles/hr
If a rectangle has a length of 10 centimeters and a width of 6 centimeters, what is the area? A) 16 cm2 B) 32 cm2 Eliminate C) 60 cm2 D) 64 cm2
Answer:
b)32 cm
Step-by-step explanation:
Answer:
C) 60 cm²
Step-by-step explanation:
A= lw
A= 10(6)
A= 10 × 6
A= 60
A parallelogram has an area of 448 square centimeters and a base length of 16 centimeters what is the height of the parallelogram?
14cm
16cm
12cm
28cm
Answer:
The answer is 28 cm.
Step-by-step explanation:
The formula for the height of a parallelogram is area divided by length, so 448/16 equals 28.
Answer:
28cm
Step-by-step explanation:
Area of a parallelogram = base x height
Given area = 448cm^2
Base = 16 cm
Therefore,
448 = 16 x h
Divide both sides by 16
448/16 = 16/16 x h
28 = h
h = 28cm
Creating a license plate with 3 letters followed by 4 digits from 0-9. (Assume you may repeat letters and numbers.)
Answer:
OHIO1801
Step-by-step explanation:
THIS LICENCE PLATE IS ORIGINALLY FROM OHIO ( I MADE IT UP (NOT THE PLACE BUT THE LICENCE PLATE) HONESTLY)
Which of the following statements is true?
a.The ratio of two integers is an irrational number.
b.An irrational number is a non-terminating, non-repeating decimal.
c.A perfect square is an irrational number.
d.Rational numbers are always positive.
IF IT WRONG NO MARK
Answer:
Option B
Step-by-step explanation:
The statement that is proven true in this question is option B or "An irrational number is a non-terminating, non-repeating decimal." A non-terminating or a non-repeating decimal is a decimal that never ends it's repeating forever and all repeating decimals are irrational numbers because the decimal cannot be expressed as a ratio with other integers so a repeating decimal is a irrational number.
Hope this helps.
6 2/3 x 3 1/3 x 5 1/4
Answer:
116 2/3
Step-by-step explanation:
Turning each of them to improper fraction, we have
6 2/3 =20/3
3 1/3= 10/3
5 1/4= 21/4
Multiply them
20/3 times 10/3 times 21/4
We have 350/3
Turning it back to a mixed fraction, we have
116 2/3
Because 350/3 is 116 remainder 2.