The rate of interest required to achieve the conditions set forth is 7.1773%.
What is the interest rate?The interest rate is the rate at which the investment increases. The formula that can be used to determine interest rate is:
g = (FV / PV)^(1/N) - 1
Where:
FV = future value = $32,000PV = present value = $8000 n = number of years4^(1/20) - 1 = 7.1773%
To learn more about interest rate, please check: https://brainly.com/question/26164549
a football player can run 13.5 yards in 4.5 seconds. which equation is used to find r, the number of yards he can run in 1 second
Answer:
3
Step-by-step explanation:
You just divide 13.5 by 4.5, and you get 3 yards per second.
mr bernstein owns 14 paintings, but has only enough wall space in his home to display three of them at any one time. How many ways can Mr Bernstein display three paintings in his home
Answer:
2,184
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
A group of researchers wants to estimate the difference in time it takes to heal enough to return to work after knee replacement surgery using two different physical therapy plans. They plan to use the data in the following table to construct a two-sample t interval.
Therapy plan A B
Mean healing time (weeks) 8.2 6.8
Standard deviation (weeks) 1.5 0.9
Number of participants 45 60
Which of the following are conditions for this type of interval?
Choose all answers that apply:
A. The times for each participant are independent of each other.
B. The distributions of times in the population are approximately normal.
C. Each sample includes equal numbers of men and women.
Answer:
A
Step-by-step explanation:
Got it right on Khan Academy.
Hope this helps!
Please mark as brainliest!
Someone help me ASAP !!!!
Answer:
ok sure wait
Step-by-step explanation:
i’ll try to mark the right answer as brainliest<: ( 20 points )
Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. a∥b, Converse of the Same-Side Interior Angles Theorem a∥b, Converse of the Alternate Interior Angles Theorem a∥b, Converse of the Corresponding Angles Theorem not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
Answer:
a∥b, Converse of the Alternate Interior Angles Theorem
If the diameter of a circle is 10 inches, what is the area of a circle?
Answer:
25[tex]\pi[/tex]
Step-by-step explanation:
because area is pi r^2
Answer:
78.54 or 25π (if in terms of pi)
Step-by-step explanation:
A = πr² = π*5² ≈ 78.53982
Find the sum of the arithmetic sequence 1, 4, 7, 10, ...,94; n=32
Answer:
Step-by-step explanation:
hello :
the sum is : Sn = n/2(U1 + Un ) and U n = U1+(n-1)r
given : U1 = 1 r=4-1=7-4=...= 3 n= 32
so : U 32 = 1+(32-1)3= 94
S32 = 32/2 (1+94) = 1520
The following table gives the partial results from a company sampling their employees to see how many years they had worked for the company. The data for both samples was right-skewed.
Department Quality assurance Service
Mean (years) 4.2 2.6
Standard deviation (years) 1.1 1.7
The company wants to use these results in a two-sample t test to see whether there is a significant difference between lengths of time for employees in the quality assurance and service departments.
Which of the following are conditions for this type of test?
Choose all answers that apply:
A. The samples represent no more than 10% percent of the employees in each department.
B. The sample includes equal numbers of employees from each department.
C. The sample includes at least 30 employees from each department.
Using the Central Limit Theorem, it is found that the condition that applies to this test is:
C. The sample includes at least 30 employees from each department.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Factor 2x2 + 7x + 10x + 35 by grouping.
Answer:
(x+5)(2x+7)
Step-by-step explanation:
x(2x+7) + 5(2x+7)
(x+5)(2x+7)
I hope this helps!!
Write an equation for a perpendicular to y = - 2 x 2 and passing through the point (-4,-5)
Y=
[tex]======================================[/tex]
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
So the slope of the given line is -2
Flop it over:
-1/2
Change its sign:
1/2
Now, let's write the equation in point-slope form:
y-y1=m(x-x1)
y-(-5)=1/2(x-(-4)
y+5=1/2(x+4)
y+5=1/2x+2
y=1/2x+2-5
[tex]\bold{y=\displaystyle\frac{1}{2} x-3}}[/tex]
[tex]==========================================[/tex]
Notes:-Hope everything's clear.Let me know if you have any questions!Enjoy your Day!Answered by:-~DnomaiD
;)
Using the equation 5x=4y, if y=10, what is x?
Answer:
x = 8
Step-by-step explanation:
plug 10 into the other equation for y then solve...
5x = 4(10)
5x = 40
x = 8 [Answer]
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Answer:
x = 8
Step-by-step explanation:
Using the equation 5x = 4y, if y = 10, what is x?
5x = 4y
5x = 4(10) <== substitute 10 for y
5x = 40
/5 /5 <== divide both sides by 5
x = 8 <== value of x, our final answer
Hope this helps!
Help picture below problem 11
The sum of all the angles of any triangle is 180 degrees
--> Therefore the missing angle is:
x = 180 - 60 - 75 = 45
Hope that helps!
The sum of the angles of a triangle is 180 degrees
--> to put that into mathematical terms
Angle O + Angle K + Angle C = 180
60 + 75 + Angle C = 180
Angle C = 45 degrees
Therefore the missing angles' measure is 45 degrees
Hope that helps!
how many times should you expect to see heads if a fair coin is tossed 3500 times?
Answer:
1750
Step-by-step explanation:
If you flip a coin, you should theoretically get heads 50% of the time and tails 50% of the time. So in this case you would get heads 1,750 times.
Find the domain & range of the relation
{(-5,13), (6,18), (2,-7), (1,4), (-3,-1)}
Answer:
Domain: -5,6,2,1,-3
Range: 13,18,-7,4,-1
Step-by-step explanation:
Domain is the independent value/ x / input
Range is the dependent value/ y / output
Which expression has a value 48?
.A) (4 + 5): 32-9 +3
.B) 4+ 5 • (32 - 9) + 3
.C) 4+ 5.3?(-9+3)
.D) 4+5•3²-9= 3
20 brainly points asap
Hey there!
Option A.
(4 + 5) * 3^2 - 9 ÷ 3^2
= 9 * 9 - 9 ÷ 9
= 81 - 1
= 80
Thus, that answer is: [incorrect]
Option B.
4 + 5 * (3^2 - 9) + 3^2
= 4 + 5 * (9 - 9) + 9
= 4 + 5 * (0) + 9
= 4 + 5(0) + 9
= 4 + 0 + 9
= 4 + 9
= 13
Thus, that answer is also [incorrect]
Option C.
4 + 5 * 3^2(-9 ÷ 3^2)
= 4 + 5 * 3^2(-9 ÷ 9)
= 4 + 5 * 3^2(-1)
= 4 + 5 * 9(-9)
= 4 + 5(9) * -1
= 4 + 45 * -1
= 4 - 45
= -41
Thus, that answer is also [incorrect]
Option D.
4 + 5 * 3^2 - 9 ÷ 3^2
= 4 + 5(9) - 9 ÷ 9
= 4 + 45 - 9 ÷ 9
= 49 - 9 ÷ 9
= 49 - 1
= 48
Therefore, your answer is: Option D.
Good luck on your assignment & enjoy your day l!
~Amphitrite1040:)
Answer:
Option D
Step-by-step explanation:
To find out which expression has a value of 48, we need to recall the PEMDAS (where: P = Parenthesis, E = Exponents, M/D = Multiplication or Division, A/S = Addition or Subtraction).
A) [4 + 5] × 3² - 9 ÷ 3²
First, simplify the expression in the parenthesis as PEMDAS
⇒ [9] × 3² - 9 ÷ 3²
Pull the "9" out of the parenthesis
⇒ 9 × 3² - 9 ÷ 3²
Simplify the exponents as PEMDAS
⇒ 9 × 9 - 9 ÷ 9
Multiply the first two terms in the expression as PEMDAS
⇒ 81 - 9 ÷ 9
Divide the last two terms as PEMDAS
⇒ 81 - 1
Finally, simplify the expression.
⇒ 80
⇒ 48 ≠ 80
B) 4 + 5 × (3² - 9) ÷ 3²
First, simplify the expression in the parenthesis as PEMDAS.
We can see here that the expression in the parenthesis includes a constant with a negative sign and an exponent. To simplify the expression, we need to simplify the exponent. Once the exponent is simplified, we can simplify the expression in the parenthesis.
⇒ 4 + 5 × (3² - 9) ÷ 3²
⇒ 4 + 5 × (9 - 9) ÷ 3²
⇒ 4 + 5 × (0) ÷ 3²
Pull the "0" out of the parenthesis
⇒ 4 + 5 × 0 ÷ 3²
Simplify the exponent as PEMDAS
⇒ 4 + 5 × 0 ÷ 9
Multiply the middle two terms as PEMDAS
⇒ 4 + 0 ÷ 9
Divide the last two terms as PEMDAS
⇒ 4 + 0
Add the two terms in the expression as PEMDAS
⇒ 4
⇒ 4 ≠ 48
C) 4 + 5 × 3²(-9 ÷ 3²)
First, simplify the expression in the parenthesis as PEMDAS
⇒ 4 + 5 × 3²(-9 ÷ 3²)
⇒ 4 + 5 × 3²(-9 ÷ 9)
⇒ 4 + 5 × 3²(-1)
*3²(-1) can also be written as 3² × -1*
⇒ 4 + 5 × 3² × -1
Simplify the exponent as PEMDAS
⇒ 4 + 5 × 9 × -1
Multiply the last three terms as PEMDAS
⇒ 4 + 5 × 9 × -1
⇒ 4 + (-45)
Add/Subtract the last two terms as PEMDAS
⇒ 4 - 45
⇒ -41
D) 4 + 5 × 3² - 9 ÷ 3²
Since there are no parenthesis in the expression, we can start simplifying this expression by simplifying the exponents.
⇒ 4 + 5 × 3² - 9 ÷ 3²
⇒ 4 + 5 × 9 - 9 ÷ 9
⇒ 4 + 5 × 9 - 9 ÷ 9
Multiply the second and the third terms as PEMDAS
⇒ 4 + 45 - 9 ÷ 9
Divide the last two terms as PEMDAS
⇒ 4 + 45 - 1
Add/Subtract the terms as PEMDAS
⇒ 4 + 44
⇒ 48
⇒ 48 = 48 ✔✔
In conclusion, we can say that option D is correct because the expression of Option D has a value of 48.
Triangle ABC has vertices A (-4,4), B(0, 3), and C(1,-1). Find the vertices of triangle A'B'C' after a
reflection across the x-axis.
Reflection is flipping. The x axis is the horizontal line. If you flip a shape over the x axis, it will still stay in the same area for the horizontal points, it's the vertical points that will change, but only their signs will because a reflection isn't moving a shapes location completely. Think of it like Flipping the page of a book. If you drew a triangle on your book page and flipped the page, it would still be in the same area just the opposite side/direction. Just make the y axis (second number in brackets) points the opposite sign to solve
-4,-4 0,-3. 1,1
Please help i need it done before tomorrow. thank you.
What is the area of the trapezoid?
Enter your answer in the box.
Answer:
Step-by-step explanation:
A = [tex]\frac{b_{1} +b_{2} }{2}[/tex] × h
~~~~~~~~
[tex]b_{1}[/tex] = 15 in.
[tex]b_{2}[/tex] = 6 + 15 + 6 = 21 in.
h = 18 in.
A = [tex]\frac{15+21}{2}[/tex] × 18 = 324 in.²
A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π4 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Answer:
Step-by-step explanation:
aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:
tanθ = opp/adj = y/x
y = xtanθ
What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):
dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Just plug all the numbers in:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
X2 -2x -24=0 is equivalent to
Answer(S):
Answer:
x= 6, -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x-6) (x+4) = 0
x = 6, x= -4
Help picture below problem 8
Answer:
Together they equal 180 l so you need to do 180-128 which equals 52. The answer is <D measures 52
Step-by-step explanation:
If x = 12 cm, what is the volume of the prism?
cm3
Answer:
4320
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) line /2
C) polar axis
D) none of these
well, let me not bore you to death on how we test it and test it.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]
so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.
Consider the function f(x)=8x3−2. If f(g(x))=x and g(f(x))=x, find g(x)
I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.
For this problem, simply find the inverse of f(x).
If you are stuck, I could provide you with a solution below...
f(x) = 8x³ - 2
y = 8x³ - 2
y + 2 = 8x³
(y + 2)/8 = x³
cube root((y + 2)/8) = x
g(x) = cube root((x + 2)/8)
The value of function g(x) after solving will be ∛(x + 2) / 2.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The value of function,
f(x) = 8x³ − 2
And, f(g(x)) = x and g(f(x)) = x
Now,
Since, f(g(x)) = x
And, f(x) = 8x³ − 2
The substitute x = g (x) in above equation we get;
f (g(x)) = 8 (g(x))³ - 2
x = 8 (g(x))³ - 2
Add 2 both side;
x + 2 = 8 (g(x))³
Divide by 8;
(x + 2)/8 = (g(x))³
Take cube root both side;
∛(x + 2)/8 = g(x)
g(x) = ∛(x + 2) / 2
So, The value of function g(x) after solving will be ∛(x + 2) / 2.
Learn more about the function visit:
https://brainly.com/question/24748644
#SPJ2
Pls help im struggling :p
When creating a histogram it is best to create a range for the different variables that are available.
So for the sake of covering all the possible ranges from 1 - 22, let's divide it into 5 categories.
0 - 5 6 - 10 11 - 15 16 - 20 21 - 25
Now that we have set ranges for the different variables, we then find the frequencies.
0 - 5 : 3
6 - 10 : 2
11 - 15 : 3
16 - 20 : 1
21 - 25 : 3
Now that we have all the values we can then create our histogram.
Taken from https://brainly.com/question/12197869
All rights reserved.
If the number of equally likely sample outcomes of a single experiment is 4, what is the total number of elements in the sample space if the experiment has 3 stages?
100 points and Brainliest for whoever answers this question correctly first.
No, this is not a test.
Yes, I would appreciate the quickest answer possible.
Answer:
[tex]\dfrac{1}{102}[/tex]
Step-by-step explanation:
Average rate of change of function [tex]f(x)[/tex] over the interval [tex]a \leq x \leq b[/tex] is:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given function:
[tex]f(x)=\dfrac{2x-2}{5x-6}[/tex]
Given interval [tex]0\leq x\leq 8[/tex] :
when [tex]x=0[/tex]:
[tex]f(0)=\dfrac{2(0)-2}{5(0)-6}=\dfrac13[/tex]
when [tex]x=8[/tex]:
[tex]f(8)=\dfrac{2(8)-2}{5(8)-6}=\dfrac{7}{17}[/tex]
Therefore, average rate of change:
[tex]\dfrac{f(8)-f(0)}{8-0}=\dfrac{\frac{7}{17}-\frac13}{8}=\dfrac{1}{102}[/tex]
Maggie is making a necklace using string and identical beads.The 12 beads fill 4 inches of the string.How many beads are in 1 inch of string
Answer:
3
Step-by-step explanation:
Divide 12 by 4 since the ratio is 12 to every 4 inches
The sum of three consecutive odd integers is 39. Find the three integers.
Answer:
11 13 15
Step-by-step explanation:
n + n + 2 + n + 4 = 39
3n + 6 =39
3n = 33
n = 11
the three odd integers are 11 , 13 ,15
if 60% of class is girls, and there are 30 students in the class. How many boys are in class?
Answer:
12
Step-by-step explanation:
60% of 30 is 18 (girls)
40% of 30 is 12 (boys)
Answer:
12 boys
Step-by-step explanation:
60% is the same as 6/10, and if you make the denominator 30, you must make the denominator multiply by three as well as the numerator. this makes the number 18/30 girls in a class. if you subtract the girls from the total number of people, you get 12 boys, or 40% of the class.
you can also find that 100% - 60% = 40%, which is equal is equal to 4/10. After it's multiplied by 3 again, it becomes 12/30 or 12 boys.