Answer :
13%
Step-by-step explanation:
Compound interest which is compounded annually calculated using the formula :
A = I( 1 + r/100)^t
Where I = invested amount
r = interest rate ; t = period ; A = final amount
If period = 9years, the rate required to triple the investment equals;
The final amount = 3 * invested amount = 3I
We now have ;
3I = I( 1 + r/100)^9
Divide both sides by I
3 = (1 + r/100)^9
Take the 9th root of both sides
3^(1/9) = (1 + r/100)^(9*1/9)
3^(1/9) = 1 + r/100
r/100 = 3^(1/9) - 1
r/100 = 1.1298309 - 1
r / 100 = 0.1298309
Multiply both sides by 100
r = 12.98309
r = 12.98 = 13%
The altitude of a triangle is 1cm shorter than the base. If the area of the triangle is 15cm2, calculate the altitude.
Answer:
5 cm
Step-by-step explanation:
We khow that the altitude of this triangle is 1cm shorter than the base
Let H be our altitude and B our base and A the area of the triangleA= (B*H)/2 ⇒ 15=(B*H)/2 H is 1cm shorter than B ⇒ B=H+1H*(H+1)/2=15 ⇒ H*(H+1)=30⇒ H²+H=30⇒H²+H-30+0that's a quadratic equation . Let's calculate the dicriminant .
Let Δ be the dicriminant
a=1b=1c= -30 Δ=b²-4*a*c = 1²-4*1*(-30)=1+4*30=121≥0 Δ≥0⇔ that we have two solutions x and y x= (-1-[tex]\sqrt{121}[/tex])/2= (-1-11)/2= -6 y= (-1+[tex]\sqrt{121}[/tex])/2= 10/2 = 5We have a negative value and a positive one
The altitude is a distance so it can't be negative
H= 5cm
A two-tailed test is one where: A. negative sample means lead to rejection of the null hypothesis B. results in either of two directions can lead to rejection of the null hypothesis C. results in only one direction can lead to rejection of the null hypothesis D. no results lead to the rejection of the null hypothesis
Answer:
Step-by-step explanation:
In a two tailed test, the alternative hypothesis contains the "unequal to" symbol. It is used when we are testing for a difference. This means that the test is regardless of direction. Therefore, the left tail and the right tail of the curve is considered when making decisions. This simply means that there are two critical regions for the test. Therefore, a two-tailed test is one where:
B. results in either of two directions can lead to rejection of the null hypothesis
Using (x + a) (x + b) = x² + (a + b) x + ab, evaluate 75 x 77
(x + a) (x + b) = x² + (a + b) x + ab
75 * 77=
=(70+5)(70+7)
=70²+(5+7)*70+5*7
=4900+12*70+35
=4900+840+35
=5775
SOMEONE PLEASE HELP ME THIS IS CONFUSING PLEASEE
An ISOSCELES right triangle has a hypotenuse of x√6 units what is the area of the triangle?
Answer:
x^2/2
Step-by-step explanation:
Alright, lets go.
Isosceles right triangle means a 45-45-90 triangle.
In a 45-45-90 triangle, the hypotenuse is [tex]\sqrt{2}[/tex] times the leg.
Therefore, the length of the leg is x√3.
The area of a triangle is b(h)/2
In a 45-45-90 right triangle, the area is equal to the length of a leg squared/2
A leg = x√3. (x√3)^2 = 3x^2
The area of the triangle is 3x^2/2
Which of the following are the correct properties of a slope? Check all that apply. A. A negative slope means that the line moves down from left to right. B. The slope of a flat line should be exactly 0. C. The slope of a flat line is smaller than the slope of a steep line with a positive slope. D. The slope of a flat line is undefined. E. A negative slope means that the line moves up from left to right.
Answer:A and D
Step-by-step explanation: I am smart trust me :)
Answer:
a. b. c.
Step-by-step explanation:
ap3x
at the end of the football season
Answer:
WHAT?
Step-by-step explanation:
VGTFTUNJMKL
Answer:
Fat monkey
Step-by-step explanation:
What ?
Question 4 Multiple Choice Worth 2 points
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
XY
3
4
5
67
89
O Initial value: 1, rate of change: 2
O Initial value: 1, rate of change: 1
O Initial value: 2, rate of change: 2
O Initial value: 3, rate of change: 2
action
Which sequence of transformations could be used to map triangle MNO onto M"N"O"? T(–2, 4) ry-axis ry-axisT(–2, 4) T(2, –4) T(2, –4)
Answer:
(A)T(–2, 4) ry-axis
Step-by-step explanation:
The graph showing triangles MNO and M"N"O" is attached below.
From the graph, the coordinates are:
M(5,-4),N(3,-2) and O(1,-3)M"(-3,0), N"(-1,2) and O"(1,1)When we transform triangle MNO by (-2,4), we obtain:
M'(3,0), N'(1,2) and O'(-1,1)
Next, we reflect M'N'O' the y-axis.
Note: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.
Therefore:
Reflection of M'N'O' accross the y-axis gives: M"(-3,0), N"(-1,2) and O"(1,1).Therefore, the sequence of transformations could be used to map triangle MNO onto M"N"O" is T(–2, 4) ry-axis.
The correct option is A.
Answer:
its B
Step-by-step explanation:
Can someone help me with this question please?
Answer:
In the Business class section not flying for first time is 13
Business class and flying first time is 7
Not in Business class and flying first time is 49
98 that are not first time or business class
Probability is 20/167. I hope this is right and helps!
A penny is dropped onto a rectangular surface. If it is equally likely for the penny to land anywhere inside the large rectangle, what is the probability that all or part of the penny will come to rest inside the shaded area? Round your answer to the nearest whole percent. A. 23% B. 26% C. 30% D. 32%
Answer:
B. 26%
Step-by-step explanation:
You have to find the area of each rectangle then divide them to find the percentage.
6x3= 18
7x10= 70
18/70= 0.2571
Move the decimal 2 spaces: 25.71%
Then you round to the nearest whole number which is 26%.
Graph the solution to this inequality on the number line.
0.3(x − 4) > -0.3
Answer:
Please refer to the attached image in the answer area.
Step-by-step explanation:
The given inequality is:
[tex]0.3(x -4) > -0.3[/tex]
To find:
The graph of inequality on the number line.
Solution:
First of all, let us simplify the inequality.
[tex]0.3(x -4) > -0.3[/tex]
Dividing it with 0.3 on the both sides:
[tex]x -4 > -1\\\text{Adding 4 on both sides}\\\Rightarrow x > 3[/tex]
i.e. all the values x > 3 will be our solution. There is no equal sign in the inequality so 3 will not be included in the solution.
Please refer to the attached image for the solution graph of the given inequality.
3 has an empty circle drawn over it which signifies that 3 is not included in the solution set.
Red line shows that all the values greater than 3 are included in the solution.
The graph of F(x), shown below, has the same shape as the graph of G(x)=x^4, but it’s shifted 3 units to the left. What’s its equation?
The number name of 70080067
In Indian System
Answer:
Seven crore eighty thousands sixty-seven.
Step-by-step explanation:
70080067
Seven crore eighty thousands sixty-seven.
One morning, Marcia works from 08 20 to 11 15.
Find how long slie works for.
Give your answer in hours and minutes.
Answer:
2:55. That's Two hours and 55 minutes.
Step-by-step explanation: From 8:20 to 11:20 would be three hours. But the actual time is five minutes less. There are 60 minutes in one hour. So change one hour to 60 minutes and subtract 5 minutes.
2:60 - :05 = 2:55
Answer:
2 hours and 55 minutes
Step-by-step explanation:
Take 11:15 and subtract 8:20
11 : 15
-8:20
------------
We need to borrow from the hours
11 becomes 10 and 1 hour = 60 minutes so add 60 to the 15
10 :75
-8:20
------------
2: 55
This is 2 hours and 55 minutes
PLEASE HELP!! will give brainliest!!
Answer:
Reason 2 : Vertical opposite angles.
Reason 3 : Vertical opposite angles.
Reason 4 : Using statement 1 and 3.
Reason 5 : Using statement 1 and 2.
Reason 6 : AA property of similarity.
Step-by-step explanation:
Statement 1 : and .
Reason 1 : Given
Statement 2 :
Reason 2 : Vertical opposite angles.
Statement 3 : [tex]\angle GEF\cong \angle DEC[/tex]
Reason 3 : Vertical opposite angles.
Statement 4 : [tex]\angle ABC\cong \angle GEF[/tex]
Reason 4 : Using statement 1 and 3.
Statement 5 : [tex]\angle ACB\cong \angle GFE[/tex]
Reason 5 : Using statement 1 and 2.
Statement 6 : [tex]\triangle ABC\cong \triangle GEF[/tex]
Reason 6 : AA property of similarity.
Hence proved.
10. Five companies employed 2340, 3455, 675, 960 and 1350 workers. The first company
laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for
every 3
THIS IS THE COMPLETE QUESTION
Five companies employed 2340, 3455, 675, 960 and 1350 workers. The first company laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for every 3. a) What was the total number of workers at the beginning c) How many people: i) Lost job ii) Got job d) What was the total number of workers finally
Answer:
a) 8780
ci) 1159
cii) 1990
d) 9611
Step-by-step explanation:
a) What was the total number of workers at the beginning?
The Total number of workers at the beginning can be calculated by adding the number of workers which are
= 2340 + 3455 + 675 + 960 + 1350
= 8780
c) How many people: i) Lost job
TO calculate the number that lost their job, we know that the first company laid off 1 worker for every 5 workers,
But the employed workers were 2340 and 1 worker laid for every 5 workers. Hence we can say that
2340/5 = 468
Therefore, 468 lost job in the first company.
To calculate for the second company,
from the question we know that Workers employed were 3455 and 1 worker laid for every 5 workers. Then we can say that
3455 / 5 = 691
Therefore, 468 lost job in second company.
After getting the number that lost their job in the two companies we can now say that the total workers that lost job:
=468 + 691 = 1159
ii) To calculate the number that Got job
We know that other three companies recruited 2 new workers for every 3, then the number of people who got job in these three companies can be calculated as;
= [(675 * 2 )+ (960 *2) + (1350 *2) ]/ 3
= (1350 + 1920 + 2700) / 3
= 5970 / 3
= 1990
Therefore, we have 1990 people that got the job.
d) the total number of workers finally can be calculated by summing up the the workers who got job in the workers at beginning then minus the number ofworkers who lost job ,
We know that the Total number of workers:
8780 number of workers at the beginning
1159 is for companies who lost job
1990 is for companies who got job
total number of workers finally:
= (8780 )+ (1990) -( 1159)
= 9611
Therefore, the total number of workers finally are 9611.
Write an equation for each translation of y
|x1.
2.5 units left
Answer:
Step-by-step explanation:
the translation of y = |x| 2.5 units to the left is:
y = |x+2.5|
Identify the slope and y-intercept of each of the following. Please help ^^^^ a. y = x + 100 b. y = 2x - 5 c. y = 0.5x
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
All 3 equations are in this form
(a)
y = x + 100
with slope m = 1 and y- intercept c = 100
(b)
y = 2x - 5
with slope m = 2 and y- intercept = - 5
(c)
y = 0.5x ( or y = 0.5x + 0 )
with slope m = 0.5 and y- intercept c = 0
Four times the difference of 17 and a number is 84.
Which equation below can be used to find the unknown number?
A) 4(17)- n = 84
B) 4 - 17n = 84
C) 17 - 4n = 84
D) 4 (17- n) = 84
Answer:
D)
Step-by-step explanation:
a number: n
difference of 17 and a number: 17 - n
4 times the difference of 17 and a number: 4(17 - n)
4 times the difference of 17 and a number is 84: 4(17 - n) = 84
Help ASAP!!
Areas of Regular Polygons
Acellus
Find the area of the regular polygon.
Round to the nearest tenth.
Vyd
[? ] yd2
Answer: 98 yards
Step-by-step explanation:
In order to find the area of a square by the diagonal, all you need to do is square the length of the diagonal and then divide by 2. 7 is half of the length, so the full length is 14. 14 squared is 196. 196 divided by 2 is 98, which is your answer.
Which of the following is equivalent to (x+4)(3x^2+2x)?
Answer:
C
Step-by-step explanation:
When expanding brackets, we distribute the left terms inside the right side brackets.
(x+4)(3x^2+2x)
(x + 4)(3x²) + (x + 4)(2x)
The reason why it is + (x + 4) is because the x has a positive sign.
Simplify the variable expression by evaluating its numerical part and enter your answer below. j + 16 - 148 + 4
Answer:
j - 128.
Step-by-step explanation:
j + 16 - 148 + 4 = j - 132 + 4 = j - 128
Hope this helps!
The graph of F(x),shown below,has the same shape as the graph of G(x)=x^4, but it is shifted 2 units to the right. What is it’s equation?
F(x) =____
Hey there! :)
Answer:
A. [tex]f(x) = (x - 2)^{4}[/tex]
Step-by-step explanation:
Recall that the transformation form of a polynomial with degree four is:
[tex]f(x) =[/tex] ±[tex]a(b(x-h))^{4} +k[/tex]
In this instance, we will need to use the h value, or the horizontal shift.
It is given that there is only a horizontal shift of 2 units to the right, or h = 2. Plug this into the equation:
[tex]f(x) = (x - 2)^{4}[/tex]
PLEASE HELP !!!! On the grid provided, draw a nonsymmetric four sided figure in Quadrant II labeled ABCD. The vertices on the figure should be integer ordered pairs. Your figure must be translated, reflected, and rotated (the order of these is your choice), your transformations must take you to Quadrant I, Quadrant III, and Quadrant IV but the final figure must end up in Quadrant I. After the first transformation, label the figure A׳B׳C׳D׳. After the second transformation, label the figure״A״B״C״D״. After the third transformation, label the figure A׳׳׳B׳׳׳C׳׳׳D׳׳׳
Answer:
The transformations included are
1) Reflection about the y-axis
2) 90° clockwise rotation
3) Reflection about the y-axis
4) Translation T(0, 21)
5) Translation T(14, 0)
Step-by-step explanation:
Reflecting a pre-image about the y-axis gives;
Point (x, y) becomes (-x, y)
Rotation 90° clockwise gives (x, y) becomes (-y, x)
Translating (x, y) by T(0, 21) gives (x, y + 21)
Translating (x, y) by T(14, 0) gives (x + 14, y).
The screen capture of the coordinates from the original solution that was having issue posting after answering is attached along side the figure chart
Which of the following is the graph of the quadratic function? y=x^2+4-12
Answer:
Graph B
Step-by-step explanation:
The solutions to a quadratic equation are the points on which we have the graph of the curve touching the x-axis
Now the first thing we will do here is to solve the quadratic equation graph;
x^2 + 4x -12 = 0
x^2 +6x - 2x -12 = 0
x (x + 6) -2(x + 6) = 0
(x-2)(x + 6) = 0
x = 2 or -6
So the graph that touches the x-axis at the points x = 2 and x = -6 is the solution to the quadratic equation
Graph B is the closest to what we have as answer
An interval estimate for the weight of a species of primates is (12, 15) kg. Find the point estimate for the species
of primates.
Answer:
12 + 15= 27/2 = 13.5 kg
Step-by-step explanation:
what is the sum of all possible multiples of 5 less than 500
Answer:
We need to find 5 + 10 + 15 + ... + 485 + 490 + 495. There are 99 numbers that are being added. To add this we can do 5 + 495, 10 + 490, 15 + 485 and so on. These pairs have a sum of 500 and since there are 98 / 2 = 49 pairs their sum is 500 * 49 = 24500. Since there is an odd number of numbers that are being added, there is one number that does not belong to a pair. That number is the 50th number in the list which is 50 * 5 = 250. Therefore the answer is 24500 + 250 = 24750.
3/5 times by 210 equals
Answer:
it equals 315
Step-by-step explanation:
What is the next number in the pattern below? 3, 5, 9, 15, 23, ___ A. 31 B. 33 C. 35 D. 37
Answer:
33. numbers are being increased by a certain number, that number being increased by 2 every time
Step-by-step explanation:
#1. The area of a square tile is 53.4cm^2. find the length of one side of the tile, rounded to the nearest 10th.
#2 which RADICAL is not a perfect square
a)5.29
b)13.69
c)1.3
d)0.09
#3 A walkway is been constructed using square cement tiles that each have an area of 15.5ft^2. Six tiles will be lined up end to end to construct a walkway. What is the total length of the walkway? Round your answer to the nearest 10th of a foot.
PLEASE ANSWER ASAP
all of them or even one would help please please
Problem 1
Answer: 7.3Explanation: Apply the square root to the area to get the side length. This only applies to areas that are squares (hence the name).
==================================================
Problem 2
Answer: C) 1.3Explanation: Use your calculator to find that choices A,B,D plugged into the square root function yield terminating decimal values. "Terminating" means "stop". This implies that they are perfect squares (though not perfect squares in the sense of whole number perfect squares which you may be used to). Choice C is the only value that has a square root that leads to a non-terminating decimal. The digits of this decimal go on forever without any pattern. The value is irrational.
sqrt(5.29) = 2.3 terminating decimalsqrt(13.69) = 3.7 terminating decimalsqrt(1.3) = 1.140175425 keeps going forever without any patternsqrt(0.09) = 0.3 terminating decimal==================================================
Problem 3
Answer: 23.6 feet approximatelyExplanation: Apply the square root to 15.5 to get roughly 3.937; this is the approximate side length of one square. Six of these tiles placed together will lead to a total length of roughly 6*3.937 = 23.622 which rounds to 23.6 feet. Like with problem 1, the square root being used like this only works for square areas.