Answer:
A) The increase population of town after 3 years is 1.2 times initial population
B) The increase population of town after 5 years is 1.4 times initial population .
Step-by-step explanation:
Given as :
The rate of growth of population of a town = r = 7.5%
Let The initial population of town = p
A ) Let The increase population of town after 3 years = P
The time period = n = 3 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 3 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]
Or, P = p × [tex](1.075)^{3}[/tex]
Or, P = p × 1.242
So, The increase population of town after 3 years = P = 1.2 times initial population
Hence,The increase population of town after 3 years is 1.2 times initial population . Answer
B ) Let The increase population of town after 5 years = P'
The time period = n = 5 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]
Or, P' = p × [tex](1.075)^{5}[/tex]
Or, P' = p × 1.4356
So, The increase population of town after 5 years = P' = 1.4 times initial population
Hence,The increase population of town after 5 years is 1.4 times initial population . Answer
in a survey 46 people which was 20% of those surveyed chose red as their favorite color how many people are surveyed
Answer:230
Step-by-step explanation:
To get to 100% you need to do 20% 5 times so if 46 people is 20% 46x5 will give you 100% of people surveyed
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
Answer:
Step-by-step explanation:
slope of line perpendicular to x=4 is 0
reqd. eq. of line is y=-5
Find the first five terms of the recursive sequence.
The first five terms of sequence is 4.5, -27, 162, -972, 5832
Solution:
Given that we have to find first five terms of recursive sequence
Given sequence is:
[tex]a_n = -6a_{n - 1}[/tex]
To find first five terms, substitute n = 2, 3, 4, 5
First term is given = [tex]a_1[/tex] = 4.5
Find second term:
Substitute n = 2 in given sequence
[tex]a_2 = -6a_{2 - 1}\\\\a_2 = -6a_1\\\\a_2 = -6(4.5) = -27[/tex]
Thus second term of given sequence is -27
Find third term:
Substitute n = 3 in given sequence
[tex]a_3 = -6a_{3-1}\\\\a_3 = -6a_2\\\\a_3 = -6(-27) = 162[/tex]
Thus third term of given sequence is 162
Find fourth term:
Substitute n = 4 in given sequence
[tex]a_4 = -6a_{4-1}\\\\a_4 = -6a_3\\\\a_4 = -6(162) = -972[/tex]
Thus fourth term of given sequence is -972
Find fifth term:
Substitute n = 5 in given sequence
[tex]a_5 = -6a_{5-1}\\\\a_5 = -6a_4\\\\a_5 = -6(-972) = 5832[/tex]
Thus the first five terms of sequence is 4.5, -27, 162, -972, 5832
PLZ ANSWER THIS
SCREENSHOT
Answer:number 3
Step-by-step explanation:
Which answer is equal to i^39
Answer:
-i
Step-by-step explanation:
see i don't mind giving my points away..Can anyone help me solve this though for a brainlest and extra points?
Answer:
a=[tex]17\sqrt{2}[/tex]
Step-by-step explanation:
As we have 2 of the angles, we can find the third. The measure of the third angle is 45 degrees.
As this is the same measure as the other, that means that the side length will be the same.
Now was have two side lengths of 17 in a right triangle, so we can use the Pythagorean theorem to find a.
Recall that the pythagorean theorem states: [tex]a^2+b^2=c^2[/tex]
In this case, a is 17, b is 17, and c is a
Knowing this, we can input our value into this formula and solve for a.
[tex]17^2+17^2=a^2\\\\289+289=a^2\\\\a=\sqrt{578} \\\\a=17\sqrt{2}[/tex]
Answer:
17sqrt2
Step-by-step explanation:
45 45 90 triangles side: hypotenuse a:a*sqrt2
17*sqrt2=17sqrt2
Tell whether each equation has one, zero, or infinitely many solutions.
5(x - 3) +6= 5x - 9
Answer:
Infinitely many
Step-by-step explanation:
Which correlation coefficient best matches the graph?
A) r = 0.91
B) r = 0.34
C) r = -0.83
D) r = -0.25
(PLEASE give right awnser. It's 11pm and Im so tired and want to get this over with. I still have other homework too :/)
Answer:
The answer is C, r = -0.83
Step-by-step explanation:
The graph has a negative slope, and the correlation between the points isn't super spread out. Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.
The correlation coefficient best matches the graph. The answer is C,
r = -0.83.
We have given that,
A) r = 0.91
B) r = 0.34
C) r = -0.83
D) r = -0.25
We have to determine the best matches graph.
What is the meaning of the correlation coefficient?The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.
The graph has a negative slope, and the correlation between the points isn't super spread out.
Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.
To learn more about the correlation coefficient visit:
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Jonathan buys 2 shirts that cost $15 and $20 respectively. He must also pay a sales tax of 8% of those costs. How
much does Jonathan pay in sales tax?
A. $1.60
B. $2.80
C. $3.50
D. $4.38
E. $4.89
How long does it take, in minutes, for a Russian Avangard Missile, which travels at a speed of Mach 27, to travel the distance from Moscow to Kabul, Afganistan, which is 3,362 kilometers?
Answer:
6.09864679092 minutes
Step-by-step explanation:
Mach 27= 33076.19km/h
3,362, at 33076.19km/h
3,362/33076.19
0.101644113182 hours
6.09864679092 minutes
Answer:
Around 6 minutes
Or in other words, fast
Answer of this question
Answer:
y = tan(x +π/2)
Step-by-step explanation:
It can be helpful to start with a simple sketch of the function you have and of the tangent function. Then, you can see the relationship.
The tangent function is always rising, has vertical asymptotes at -π/2 and π/2, and has a zero crossing at x=0.
The function we want is always rising, has vertical asymptotes at x=0 and x=±π, and a zero crossing at x=-π/2.
We can create the function we want by shifting the tangent function to the left by π/2. The formula that does that is ...
y = tan(x +π/2)
In the video, I drop a ball off a three-story balcony. We know that objects in freefall follow the equation for height h, in
meters, h = – 4.9t' + c, where t is time in seconds, and is the initial height. A student timed the drop at 1.27
seconds.
Use this to determine the height from which the ball was dropped, to at least 2 decimal places.
Answer:
The initial height from which the ball was dropped = 7.90 meters
Step-by-step explanation:
The correct question is:
In the video, I drop a ball off a three-story balcony. We know that objects in free fall follow the equation for height h, in meters, [tex]h = -4.9t^2 + c[/tex], where [tex]t[/tex] is time in seconds, and [tex]c[/tex] is the initial height. A student timed the drop at 1.27 seconds.
Use this to determine the height from which the ball was dropped, to at least 2 decimal places.
Solution:
The height [tex]h[/tex] of the free falling ball is represented by the equation as:
[tex]h=-4.9t^2+c[/tex] where [tex]t[/tex] is time in seconds, and c is the initial height.
To determine the initial height from which the ball was dropped.
The drop was timed at 1.27 seconds, we will plugin [tex]t=1.27[/tex] in the given height function to find [tex]h(1.27)[/tex]
[tex]h(1.27)=-4.9(1.27)^2+c[/tex]
[tex]h(1.27)=-7.90+c[/tex]
Since, the drop is timed at 1.27 seconds, so in the given time the ball will reach the ground, making [tex]h(1.27)=0[/tex]
So, we have.
[tex]0=-7.90+c[/tex]
Adding both sides by 7.90 to solve for [tex]c[/tex].
[tex]0+7.90=-7.90+7.90+c[/tex]
[tex]7.90=c[/tex]
∴ [tex]c=7.90\ m[/tex]
Thus, the initial height from which the ball was dropped = 7.90 meters
All of the following must be true statements except:
m∠RPS = m ∠WPR
m∠RPS + m∠ SPU= 180
m∠ SPT = m∠ UPT
We need to find the false statement.
The first one is true (m<RPS=m<WPR because RU⊥SW).
The second statement is true because the two angles make a linear pair and are supplementary.
The third one is false because we only know that the angle pair is complimentary. Their measures are not equal.
answer: m∠SPT=m∠UPT
Does anyone know how to do these maths question???
Answer:
Part 1) [tex]f(g(x))=3(x^2)+2[/tex]
Part 2) [tex]g(f(5))=289[/tex]
Step-by-step explanation:
we know that
A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function
we have
[tex]f(x)=3x+2[/tex]
[tex]g(x)=x^{2}[/tex]
Part 1) Determine f(g(x))
To find f(g(x)) substitute the function g(x) as the variable in function f(x)
so
[tex]f(g(x))=3(x^2)+2[/tex]
Part 2) Determine g(f(x))
To find g(f(x)) substitute the function f(x) as the variable in function g(x)
so
[tex]g(f(x))=(3x+2)^2[/tex]
For x=5
[tex]g(f(5))=(3(5)+2)^2[/tex]
[tex]g(f(5))=289[/tex]
A large cheese pizza costs $11.99 a medium cheese pizza costs $8.99 how much do 2 large and 3 medium pizzas cost? (Estimate to)
Answer:
$50.95
Step-by-step explanation:
2(11.99)+3(8.99)=50.95
Also for:
P. Q. R.
F. T. T
F. T. F
F. F. T
F. F. F
Answer:
See below table
Step-by-step explanation:
[tex]\begin{array}{cccccccc}p&q&r&\sim q&\sim q\rightarrow p&r\vee(\sim q\rightarrow p)&\sim p&[r\vee (\sim q\rightarrow p)]\rightarrow \sim p\\ \\ \\ \\T&T&T&F&T&T&F&F\\ \\T$&T&F&F&T&T&F&F\\ \\T&F&T&T&T&T&F&F\\ \\T&F&F&T&T&T&F&F\\ \\ \\ \\F&T&T&F&T&T&T&T\\ \\F&T&F&F&T&T&T&T\\ \\F&F&T&T&F&T&T&T\\ \\F&F&F&T&F&F&T&T\end{array}[/tex]
Answer:
?
Step-by-step explanation:
What is the slope of (-9,9) (-2,1)
｡☆✼★ ━━━━━━━━━━━━━━ ☾
slope = difference in y/difference in x
Substitute values in:
slope = (1 - 9)/(-2- (-9)
slope = -7/7
slope = -1
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Select two options that correctly describe the graph.
A. discrete
B. continuous
C. linear
D. nonlinear
Answer:
[see pdf]
Step-by-step explanation:
The graph makes a straight line, not a curve, so it is linear.
However, the graph has only points, not a full line, so it's also discrete.
(also yes I meant of instead of on in the pdf)
Answer:
A. discrete, C. linear
Step-by-step explanation:
By analysing the graph, it is evident that model is discrete since there is only information of certain points and shows a linear behavior, as there is a constant rate between dependent and independent variable. So, the right choices are A and C.
A rectangle has a heigh if 4x^3 and a width of x^3+3x^2+2x
Answer:
Area = [tex]4x^6+12x^5+8x^4[/tex]
Step-by-step explanation:
The Complete Question:
A rectangle has height [tex]4x^3[/tex] and width [tex]x^3+3x^2+2x[/tex]. What is the area of the rectangle in terms of x?
Solution:
The formula for the area of a rectangle is:
Area = Height * Width
Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:
[tex]A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4[/tex]
This is the area of the rectangle.
The angle of elevation of a ladder leaning against a wall is 60 degree and the foot of the ladder is 4.6 m away form the wall.The length of the ladder is
Answer:
The length of the ladder is 9.2m
Step-by-step explanation:
2 sin 2theta = root 3 , find the value of theta
Answer:
θ= 30° or θ= 60°
Step-by-step explanation:
Please see attached picture for full solution.
Since √ 3/2 is positive, look at first 2 quadrant. (CAST diagram)
A boat traveled 504 miles downstream and back. The trip downstream took 14 hours. The trip back took 21 hours. What is the speed of the boat in still water? What is the speed of the current?
Answer:
The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.
Step-by-step explanation:
Let's say b is the speed of the boat in still water, and c is the speed of the current.
Distance = rate × time
Going downstream:
504 = (b + c) × 14
36 = b + c
Going upstream:
504 = (b − c) × 21
24 = b − c
Two equations, two variables. Solve with substitution or elimination. To use elimination, add the equations together.
60 = 2b
b = 30
Plug into any equation to find c.
36 = b + c
36 = 30 + c
c = 6
The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.
The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Let the speed of the boat in still water be x and the speed of water be y.
A boat traveled 504 miles downstream and back. The trip downstream took 14 hours. Then the equation will be
x + y = 504 / 14
x + y = 36 ...1
The trip back took 21 hours. Then the equation will be
x - y = 504 / 21
x - y = 24 ...2
Add equations 1 and 2, then the value of x will be
2x = 36 + 24
2x = 60
x = 30 miles per hour
Then the value of y will be
30 - y = 24
y = 6 miles per hour
The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.
More about the solution of the equation link is given below.
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Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by SAS?
Answer:
NM and FG
Step-by-step explanation:
To make sure the triangles are congruent by SAS, Ebony needs to compare the lengths of two sides and the measure of the included angle of the triangles.
Explanation:In order to make sure the triangles are congruent by SAS (Side-Angle-Side), Ebony would need to compare the lengths of two sides and the measure of the included angle of the triangles.
Specifically, Ebony would need to compare:
The lengths of segment EF and segment ONThe measure of ∠MON and ∠GEFIf the length of segment EF is equal to segment ON and the measure of ∠MON is equal to ∠GEF, then the triangles will be congruent by the SAS postulate.
Learn more about triangles are congruent here:https://brainly.com/question/22062407
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Helppppppppppppppppp
Answer:
π(6²)
Step-by-step explanation:
The base of the cone is a circle with area (A) calculated as
A = πr² ← r is the radius
Here diameter = 12 , hence r = 12 ÷ 2 = 6, thus
A = π(6²)
what is 100000 less than 5 million
Answer: 4,900,000
Step-by-step explanation:
5 million - 100 thousand = 4.9 million
Latasha is getting married.She is inviting 300 people and is sending formal invitations to her wedding. If it takes her 90(or 1.5 minutes) to stuff and address each envelope, how much time will it take to complete her invitations?THE ANSWER MUST BE IN HOURS AND MINUTES
Answer:
7 hours, 30 minutes
Step-by-step explanation:
90 seconds times 300 = 27,000 seconds. Divided by 60 equals 450 minutes. Divided by 60 equals 7 hours, 30 minutes
Answer:
it will take 7 hours and 30 minutes to complete her invitations
Step-by-step explanation:
time taken for one envelope= 90 secs
time taken for 300 envelopes= 90*300= 27000 secs
Converting it into minutes = 27000/60= 450 minutes
Converting 450 minutes to hours = 450/60= 7.5 hours
Find the value of x.
124°
95°
92°
143
Answer:
92 are the value of x I think
A srtaight line l has the equation of 2y-6x=-8 what is the gradient of l
Answer:
gradient = 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
Rearrange 2y - 6x = - 8 into this form
Add 6x to both sides
2y = 6x - 8 ( divide all terms by 2 )
y = 3x - 4 ← in slope- intercept form
with gradient m = 3
Type the correct answer in each box.
A circle is centered at the point (-7, -1)
The radius of the circle is
Answer:
Part 1) The radius is [tex]r=17\ units[/tex]
Part 2) The points (-15,14) and (-15,-16) lies on the circle
Step-by-step explanation:
The correct question is
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is ____units.
The point (-15,
?) ) lies on this circle
step 1
Find the radius of the circle
we know that
The distance from the center to any point on the circumference is equal to the radius.
we have
[tex](-7,-1),(8,7)[/tex]
Find the distance
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}\\r=\sqrt{(8)^{2}+(15)^{2}}\\r=\sqrt{289}\\r=17\ units[/tex]
step 2
The point (-15,y) lies on the circle
we know that
If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle
The equation of the circle is
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
The center is (-7,-1) an the radius is 17 units
substitute
[tex](x+7)^{2}+(y+1)^{2}=17^{2}\\(x+7)^{2}+(y+1)^{2}=289[/tex]
substitute the x-coordinate of the point and solve for the y-coordinate
For x=-15
[tex](-15+7)^{2}+(y+1)^{2}=289\\(-8)^{2}+(y+1)^{2}=289\\64+(y+1)^{2}=289\\(y+1)^{2}=289-64\\(y+1)^{2}=225[/tex]
square root both sides
[tex](y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16[/tex]
therefore
The points (-15,14) and (-15,-16) lies on the circle
see the attached figure to better understand the problem
The question relates to the properties of a circle in a coordinate system, where the circumference and area can be calculated using the radius. The circumference of a circle is found using C = 2πr, and the area is A = πr². Without a given radius, these formulas are a guide for any calculations that may be done once the radius is known.
Explanation:The question asks about the properties of a circle given its center and radius, which fall under the topic of Geometry in Mathematics. No specific value for the radius is provided, so the answer should include an explanation of how one might calculate various properties of a circle, such as the circumference or area, given a radius.
Understanding the Circle
A circle with its center located at (-7, -1) means it is positioned on a coordinate system at that point. If a radius was provided, the circumference of the circle would be calculated using the formula C = 2πr and the area using A = πr², where 'r' represents the radius of the circle and 'π' (pi) is approximately 3.14159. For example, if r = 1.2 m, the area calculated to two significant figures would be A = 4.5 m².
For a circle to fit perfectly inside a square, its diameter should be equal to the side of the square; this implies that a = 2r. The area of the square is a² = 4r², and a circle inside this square would have an area of approximately three-quarters of the square, or near πr². The perimeter (circumference) of the circle is somewhat close to 6r as the perimeter should be 2πr.
The florist makes the greatest number of identical
arrangements with the lilies and the daisies. Which
combination describes the arrangements?
6 arrangements with 10 lilies and 6 daisies
6 arrangements with 6 lilies and 10 daisies
12 arrangements with 10 lilies and 6 daisies
12 arrangements with 5 lilies and 3 daisies
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation: