The number of years will the population reach 14,652 will be 500 years.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The growth in the population of a city can be seen using the formula given below.
[tex]\rm P(t) = 9768 \times e^{0.003 \times t}[/tex]
Where t is the number of years.
The number of years will the population reach 14,652 will be given as,
[tex]\rm 14652 = 9768 \times e^{0.003 \times t}\\\\e^{0.003 \times t} = 1.5[/tex]
Take natural log on both sides, then we have
0.003 × t = 1.5
t = 1.5 / 0.003
t = 500 years
The number of years will the population reach 14,652 will be 500 years.
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If two chords are the same distance from the center of a circle then they are
If two chords are the same distance from the center of a circle then they are congruent.
Given that, two chords are the same distance from the center of a circle.
What is the chord on a circle?The chord of a circle is a line that connects two points that are located on the circumference of the circle. These two points can be located anywhere on the same circumference.
Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle.
Hence, if two chords are the same distance from the center of a circle then they are congruent.
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Tracy pays $8.50 of her monthly life insurance premium and her employer covers the rest of her monthly premium is $32.25 what is the annual value to Tracey of this benefit
Final answer:
Tracy's employer pays $23.75 each month towards her life insurance premium. The annual value of this benefit to Tracy is $285, calculated by multiplying the monthly employer contribution by 12.
Explanation:
The question is asking to calculate the annual value of the benefit that Tracy receives from her employer for her life insurance. Tracy pays $8.50 monthly and her employer covers the remainder, making the total monthly premium $32.25. To find the annual value of the benefit, we need to first determine how much her employer pays each month and then multiply this by 12 to get the annual value.
First, we subtract Tracy's contribution from the total premium:
$32.25 - $8.50 = $23.75
This is the monthly contribution by the employer. Now, to find the annual value, we multiply the monthly employer contribution by 12:
$23.75 × 12 = $285. Therefore, the annual value of the benefit that Tracy receives is $285.
Calculate the average rate of change for the given graph from x = –2 to x = 0 and select the correct answer below.
the average rate of change for the given graph from x = -2 to x = 0 is:
3
Step-by-step explanation:We know that the average rate of the graph of the function f(x) form x=a to x=b is calculated by the formula:
[tex]Average\ Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}[/tex]
Here we have:
a= -2 and b=0
Also, from the graph of the function we have:
f(a)=0 and f(b)=6
Hence, the average rate of change of the graph from x= -2 to x=0 is:
[tex]Average\ Rate\ of\ change=\dfrac{6-0}{0-(-2)}\\\\i.e.\\\\Average\ Rate\ of\ change=\dfrac{6}{2}\\\\i.e.\\\\Average\ Rate\ of\ change=3[/tex]
Hence, the answer is: 3
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use? a. Recording all of her daily expenditures in an organizational computer program. b. Keeping and collecting receipts for everything she buys. c. Tracking and collecting her bank and credit statements every month. d. Carrying a notebook and immediately recording all of her transactions in it.
Answer:
the answer is d
Step-by-step explanation:
everybody else keeps getting it wrong, the answer is d
In what time will $400 amount to $512 if the simple interest is calculated at 14% p.a.
Ed counts 23 black cars, 9 red cars, 17 blue cars, 25 white cars and 21 silver cars during 20 minutes of watching. How many more white and blue cars are there than silver and red cars?*
You are asked to draw an equiangular rhombus, an equilateral rectangle, and a parallelogram with four right angles. will all three figures be squares?
All the three figures given in the problem cannot be squares.
What is a parallelogram?A parallelogram is a type of quadrilateral of which the opposite sides are equal and parallel. A diagonal of a parallelogram divides it into two congruent triangles.
Given that,
There are an equiangular rhombus, an equilateral rectangle, and a parallelogram with four right angles.
They can be explained one by one as follows,
(a) A rhombus has all the four sides as equal and its opposite sides are parallel.
When all the angles of a rhombus becomes equal, its each angle is a right angle.
It implies that it will have all angles equal to right angle and all sides are equal as well.
Thus, an equiangular rhombus is a square.
(b) A rectangle has all its angle equal to right angle.
Opposite sides are equal and parallel.
When all the sides become equal, it will be a square.
(c) A parallelogram has its opposite sides as equal and parallel.
When all the angles become right angles, it can be a rectangle.
Hence, an equiangular rhombus and an equilateral rectangle can be a square but a parallelogram with four right angles cnnot be so.
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Write an expression that represents "the difference of eight and two, added to x"
pease help
1) where is the y intercept of any direct variation equation?
2) circle the equation that is a direct variation equation.
1) y=7-3x
2)3x-7y=1
3) 3x-7y=0
4) 3y=7x-1
3) what is the direct variation equation if y=8 and x = 4?
4) what is the direct variation equation if y =-5 and x = 7 /
1. where is the y intercept of any direct variation equation?
A direct variation equation is one in which the general form is:
y = k x
where k is the constant of proportionality
The y-intercept in this case is therefore zero so it is located on the origin (0, 0)
2. The equation which is a direct variation is:
3) 3x-7y=0
Because we can write this as:
y = (3/7) x
3. what is the direct variation equation if y=8 and x = 4?
We solve for the value of k since we know that:
k = y/x
k = 8/4 = 2
So the equation is:
y = 2x
4. what is the direct variation equation if y =-5 and x =
7?
We also solve for the value of k since we know that:
k = y/x
k = -5/7
So the equation is:
y = (-5/7) x
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.
The reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning is:
When a pair of lines intersect, the vertical angles are congruent.
Step-by-step explanation:The vertical angles are the opposite angles that are formed by the intersection of two lines. They are also known as Vertically opposite angles.
We know that when a pair of lines intersect then the vertical angles are always congruent.
However the measure of the angles may be acute or obtuse or right angle.
The same could be seen with the help of the figure attached to the answer.
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In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent?
Final answer:
An independent system of linear equations has two lines that intersect at exactly one point. If the slope of one line is the negative reciprocal of the other, the lines are perpendicular, indicating they intersect once and the system is independent.
Explanation:
If the slope of one line in a system of linear equations is the negative reciprocal of the slope of the other line, this indicates that the two lines are perpendicular to each other. Perpendicular lines intersect at one point and therefore, the system of equations is independent. An independent system has a single unique solution, meaning that there is exactly one point where the two lines cross.
In terms of graphs and equations, the slope or 'm' in the equation y = mx + b represents the rate at which the dependent variable changes with respect to the independent variable. The negative reciprocal relationship between slopes of two lines means that one will rise (positive slope) and fall (negative slope) at the same rate but in opposite directions, ensuring they intersect just once unless the y-intercepts (b) are also identical, which would make them the same line (dependent system) rather than intersecting lines.
drag each label to the correct location on the table each label can be used more than once but not all labels will be used
this is the question...
WHAT IS 6.4 DIVIDED BY 43.52
Final answer:
To divide 6.4 by 43.52, the approximate quotient is 0.09238.
Explanation:
To divide 6.4 by 43.52, you can simply perform the division operation. Here are the steps:
Set up the division problem as follows: 6.4 ÷ 43.52.Divide the decimal part of the dividend (6.4) by the divisor (43.52). The quotient will have the same number of decimal places as the dividend. In this case, divide 4 by 43, which equals approximately 0.09238.Therefore, 6.4 divided by 43.52 is approximately 0.09238.
A photo 5 inches wide and 8 inches long is enlarged. How long is the new photo if it is (1)10 inches; (2)15 inches; (3)8 inches wide?
Answer:
1.16 in
2.24 in
3.12.8 in
Step-by-step explanation:
We are given that
Width of photo=5 in
Length of photo=8 in
We have to find the length of new photo in each case.
1. Let x represent the width and y represents the length of photo.
When width increase then length of photo is also increases then it is direct proportion.
[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]
Substitute the values then we get
[tex]\frac{5}{8}=\frac{10}{y}[/tex]
[tex]y=\frac{10\times 8}{5}=16[/tex]
Hence, the length of photo=16 in
2.Width=x=15 in
Again using the formula
[tex]\frac{5}{8}=\frac{15}{y}[/tex]
[tex]y=\frac{15\times 8}{5}=24[/tex]
Hence, the length of new photo=24 in
3. Width =x=8 in
Substitute the values in the given formula
[tex]\frac{5}{8}=\frac{8}{y}[/tex]
[tex]y=\frac{8\times 8}{5}=\frac{64}{5}=12.8[/tex]
Hence, the length of new photo=12.8 in
PLEASE HELP.
On a road, a bike sign in the shape of an isosceles trapezoid is to be painted. The sign and its dimensions are shown below. What is the area of the sign?
A.24 square feet
B.28 square feet
C.30 square feet
D.32 square feet
Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?
What are the x and y intercepts of the line described by this equation? 4x-3y=12.3
Solve for x. 5(x + 1) = 4(x + 8) x = 7 x = 17 x = 27 x = 37
The value of x in 5(x + 1) = 4(x + 8) is 27.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
5(x + 1) = 4(x + 8)
Now, applying distributive property
5x+ 5 = 4x+ 32
5x - 4x = 32- 5
x= 27
Hence, the value of x is 27.
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factor 9x^2 -5 . using difference of squares
In a particular class of 31 students, 12 are men. What fraction of the students in the class are women
The measure of one angle is three times the measure of its complement
What is the coefficient of the fourth term in the expansion of (x + 3)4?
Final answer:
The coefficient of the fourth term in the expansion of (x + 3)⁴ is calculated using the binomial theorem, which results in a coefficient of 108.
Explanation:
To find the coefficient of the fourth term in the expansion of (x + 3)⁴, we can use the binomial theorem. The binomial theorem states that when a binomial is raised to a power, the expansion consists of terms in the form of [tex]C(n, k) \times a^{n-k} \times b^k[/tex], where C(n, k) is the binomial coefficient. In our case a = x and b = 3, and n = 4.
For the fourth term where k = 3, the term would be [tex]C(4, 3) \times x^{4-3} \times 3^3[/tex]. The binomial coefficient C(4, 3) is equal to 4 because there are four ways to choose three items out of four. Therefore, the coefficient is 4 × 3³ = 4 × 27 = 108. So, the coefficient of the fourth term in the expansion of (x + 3)⁴ is 108.
Which line is parallel to line r?
line p
line q
line s
line t
Write the expression as a single natural logarithm.
3 ln 2 + 6 ln y
Answer:
[tex]ln(8y^{6})[/tex]
Step-by-step explanation:
3ln(2)+6ln(y)
= [tex]ln(2^{3} )+ln(y^{6})[/tex]
= [tex]ln(8 )+ln(y^{6})[/tex]
= [tex]ln(8*y^{6})[/tex]
= [tex]ln(8y^{6})[/tex].
30 POINTS!!
Which construction correctly shows how to bisect ∠X?
An angle bisector is a ray, segment, or line that divides a given angle into two angles of equal measure. Therefore, the correct answer is option C.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.
Steps to Construct an Angle Bisector:
Step 1: Draw any angle, say ∠ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F.
Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Therefore, option C is the correct answer.
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A machine produces 584 units in 8 hours. how many units does it produce in 2 hours?
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
584 units = 8 hours
1 hour = 73 units
2 hours = 146 units
The number of units produced in 2 hours is 146 units.
What is a unit rate?
It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A machine produces 584 units in 8 hours.
This means,
584 units = 8 hours
Divide both sides by 8.
1 hour = 73 units
Now,
1 hour = 73 units
Multiply 2 on both sides.
2 hours = 146 units
Thus,
The number of units produced in 2 hours is 146 units.
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An organization founded by businesses in a specific industry for the purpose of collaboration between companies is called a(n):
Answer:
The answer is trade association.
Step-by-step explanation:
Such organizations are founded to encourage trade and collaboration between companies. These are also known as industry trade group or business association and is funded by businesses that operate in a particular industry.
Scott drove to his friends house and back.on the trip there he drove 72km/h and on the return trip he went 60 km/h. How long did the trip there take if the return trip took six hours?
Joey saved $2 today. if he doubles the number of dollars he saves each day, how many days, including today, will it take him to save more than $500?
By saving double the amount saved on the previous day starting with $2 in 8 days Joey will have $500.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, Joey saved $2 today. If he doubles the number of dollars he saves each day.
This can be formed as a geometric sequence with common ratios(r) = 2.
a₁ = 2, We know the sum of a geometric series is [tex]S_n = \frac{a_1(r^n - 1)}{r - 1}[/tex].
∴ 500 = 2(2ⁿ - 1)/(2 - 1).
2ⁿ - 1 = 250.
2ⁿ = 251.
[tex]log_22^n = log_2251[/tex].
n = 7.97 Or approximately in 8 days.
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