Given:
Total invested amount = $5400
Rate of interest for first account = 14%
Rate of interest for second account = 6%
Total interest after one year = $580
To find:
The amount invested in each account.
Solution:
Let the amount invested in the first account be $x, then the amount invested in the second account is $(5400-x).
Total interest = 14% of $x + 6% of $(5400-x).
[tex]580=\dfrac{14}{100}x+\dfrac{6}{100}(5400-x)[/tex]
Multiply both sides by 100.
[tex]58000=14x+6(5400-x)[/tex]
[tex]58000=14x+32400-6x[/tex]
[tex]58000-32400=8x[/tex]
[tex]25600=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{25600}{8}=x[/tex]
[tex]3200=x[/tex]
Now,
[tex]5400-x=5400-3200[/tex]
[tex]5400-x=2200[/tex]
Therefore, the amount invested in first account is $3200 and the amount invested in the second account is $2200.
Part B
You will now perform the construction of a tangent to a circle using modern tools.
Open GeoGebra C, and complete each step below. If you need help, follow these
instructions for using GeoGebra.
1. Create a circle with a center at point A with a radius of your choice.
2. Now create a point outside of circle A, and label it point B. Draw a line segment
connecting points A and B. Find the midpoint of line segment AB, and label it
point C.
3. Using point C as the center, create a circle that passes through point A.
4. Circle A and circle C intersect at two points. Find these intersection points, and
label them points D and E.
5. Draw rays from point B through point D and from point B through point E. Also
draw line segments connecting points A and D and points A andis.
Take a screenshot of your image, save it, and insert the image in the space provided
Answer:
This is what I put ! I got an A! (Although the extra rays I don't think are needed)
Step-by-step explanation:
The figure is attached below
What is Tangent?In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. A tangent of a circle is defined as a straight line that touches or intersects the circle at only one point. A tangent is a line that touches the edge of a curve or circle at one point, but does not cross it.How to solve this problem?The steps are as follow:
Create a circle with a center at point A with a radius of your choice.Now create a point outside of circle A, and label it point B. Draw a line segment connecting points A and B. Find the midpoint of line segment AB, and label it point C.Using point C as the center, create a circle that passes through point A.Circle A and circle C intersect at two points. Find these intersection points, and label them points D and E.Draw rays from point B through point D and from point B through point E. Also draw line segments connecting points A and D and points A andis.From the above steps we have drawn the figure which is attached below
Learn more about tangent here:
https://brainly.com/question/4470346
#SPJ2
what is the measure of angle xyz?
Answer:
The answer is B. 93
Step-by-step explanation:
186/2 is 93
Answer:
welp now i can add my answer although the other dude got it before me so yea other person is right
Step-by-step explanation:
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Marie found that 4 bags of leaves weigh 6 pounds and 8 bags of leaves weigh 12 pounds. She made a graph to help her find the weight of other numbers of bags. On a coordinate plane, a line is drawn through points (4, 6) and (8, 12). Which ordered pair follows the pattern in the graph? (2, 4) (3, 4) (6, 8) (6, 9)
Answer:
D 6,9
Step-by-step explanation:
Round 665749 to the nearest hundred thousand?
I need help with solving this equation.
Answer:
66 m².
Step-by-step explanation:
From the question given above, the following data were obtained:
Diagonal 1 (d₁) = 11 m
Diagonal 2 (d₂) = 12 m
Area (A) =?
The area of a rhombus when the diagonals are given can be obtained as follow:
A = ½(d₁d₂)
A = ½ × (11 × 12)
A = ½ × 132
A = 66 m²
Thus, the area of the rhombus is 66 m²
Mimi is tacking 6 posters on her wall. Every poster needs a tack in each corner. What is THE LEAST number of tacks Mimi needs to hang the posters so that each can be seen completely?
Answer:
36 if the posters have 3 corners
Step-by-step explanation:
you would just multiply the corners by 6
Olaf wants to buy a guitar that costs $600. He makes $3 per day. How many days will it take Olaf to save enough money to buy the guitar
Answer:
200 days
Step-by-step explanation:
600/3 = 200
Answer:
200 days
Step-by-step explanation:
Simple: You divide the cost of the guitar by the amount he gets paid per day. Hope this helps :)
Ava swam for 154 minutes during her first week of vacation. In her two weeks of vacation, she swam for a total of 357 minutes. How many more minutes did she swim for in the second week than in the first week?
Answer:
Ava swam 203 more miles
Step-by-step explanation:
357-154=203
Kammys mom gave her $85 to go shopping if she spent $118 how much of her own money did curry use
Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour to complete. List the lengths of time in order from least to greatest.
Rewrite the fractions to have a common denominator:
1/3 = 10/30
4/6 = 20/30
1/5 = 6/30
Now compare the numerators and list from smallest to largest:
6/30, 10/30, 20/30
The order would be:
1/5, 1/3, 4/6
Answer:
1/5, 1/3, 4/6
Step-by-step explanation:
The bigger the fraction denominator the smaller is.
1. A company has a cash portfolio measured in millions. The drift is 0.1 per month, variance is 0.16per month. The initial cash is 2.0. a) Find the probability distribution after 6 months and after 1 year. b) Find the probability of a negative cash position at the end of 6 months and the end of 1 year. c) At what time in the future is the probability of a negative distribution greatest.
Answer:
Step-by-step explanation:
From the information given:
The probability distribution at the end of 6 months is determined as follows:
After 6 months;
Mean of probability distribution = value of Initial cash + [tex]\alpha[/tex]T
=2.0 +(0.1 × 6)
=2.6
After 6 months;
The probability distribution's standard deviation is estimated by using the following formula:
Standard deviation:
[tex]= b\sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{6}[/tex]
= 0.9798
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 2.6
Standard deviation 0.9798
Variance 0.96
After 12 months, the probability distribution is as follows:
Mean = value of Initial cash + [tex]\alpha[/tex]T
= 2.0 +(0.1 × 12)
= 3.2
The standard deviation is:
The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{12}[/tex]
= 1.3856
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 3.2
Sandard deviation 1.3856
Variance 1.92
b)
in 6-month distribution, the probability of the negative value of the cash position is as follows.
Now, for us to find the negative cash distribution;
We need to estimate the z -scores value.
The z-score inform us greatly on the concept of how far a particular data point is from the mean.
For a normal distribution;
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
Here;
the value of x = zero as a result that if it exceeds zero. the cash position will be negative.
∴
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]
[tex]z = -2.6536[/tex]
Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.
As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.
For 12 months distribution:
The Probability of negative cash position is calculated as follows:
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]
Using the standard distribution tables,
N(-2.31) equals 0.0104 or 1.04 percent.
As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year
c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]
This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.
To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.
The first step is to go over the z-score formula in more detail, as seen below.;
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]
Now, compute the derivative of this equation with respect to T as follows:
[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]
Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:
[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]
As a result, the time period in which achieving a negative cash condition is = 20 months.
What type of world would you want to escape to right now if you could ?
besides 9 and 1 what is one factor of 9
Answer:
3
Step-by-step explanation:
3 times 3 is equal to nine
Have a good day!
Answer:
3
Step-by-step explanation:
This is the answer.:)
The factors of 9 are : 1, 3, 9.
PLS ANSWER ASAP! Only answer if you are sure that it is correct & no links or i will report you
What is the value of the expression 8 divided by 12?
Answer:
2/3 or .66666666
Step-by-step explanation:
In football, a field goal is kicked from a position on the field
through a goal post that is 360 inches beyond the goal line. If a
field goal is kicked from the 38-yard line, what is the distance in feet to the goal post
Answer:
144 ft. i just had this question on my test .
Step-by-step explanation:
2. If GFE~GJH, find the value of FG.
Answer:
77 unitsStep-by-step explanation:
Given two similar triangles.
Corresponding parts of similar figures have same ratio.
Use ratios to find the value of x:
(4x - 5)/(x + 7) = 35/12.5(4x - 5)/(x + 7) = 14/55(4x - 5) = 14(x + 7)20x - 25 = 14x + 9820x - 14x = 98 + 256x = 123x = 123/6x = 20.5Find the value of FG:
FG = 4*20.5 - 5 = 77When graphing a system of equations with infinitely many solutions, the slopes of the two lines will be ________.
Please help answer !:)
Will give brainlst!!
Have a nice day
Answer:
10, exponents, 10, expression
Step-by-step explanation:
n exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval
The exponential grows at half the rate of the quadratic.
The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic.
The exponential grows at four times the rate of the quadratic.
https://brainly.com/question/4184462
Answer:
the answer is B)
Step-by-step explanation:
edg2021 :>
The equation for the perimeter around Claire's garden is a:
Group of answer choices
Linear Function
Exponential Function
Quadratic Function
Absolute Value Function
Answer:
Linear Function
Step-by-step explanation:
I just took the test and got it right.
Given f(x) = -x^2 - 2x + 4, find each of the following,
Symmetric point:
Minimum of f:
Maximum of f:
Is f a one-to-one
Does f have an inverse?
Increasing on
Decreasing on
Answer:
Symmetric point: x = -1; (-1, 5)
Minimum of f: None; approaches -∞.
Maximum of f: y = 5.
Is f(x) a one-to-one: No, it fails the horizontal line test and is not injective.
Increasing from: -∞ to -1; (-∞, -1)
Decreasing from: -1 to ∞. (-1, ∞)
Answer:
Given f(x) = -x^2 - 2x + 4, find each of the following,
Step-by-step explanation:
f(x) = -x²-2x+4
f(2) = (-2)²-2×2+4
f(2) = 4-4+4
f(2) = 4
Acellus
Find the measure of < 4.
44
158°
{
*4 = [?]
Fnter
<4=22°
Answer:
<4+158=180 co interior angle
<4=180-158=22°
Answer:
solution given:
<4+<158°=180°[co- interior angle]
<4=180°-<158°=22°
<4=22° is your answer
How many times greater is the value of the 8 in 382,000 than the value of the 8 in 38,200
Answer:
10 times
Step-by-step explanation:
382,000 divided by 38,200 = 10
PLEASE HELPS!!!!!!!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST AND EXTRA POINTS!!!!!!!!!!!!!!!!!!!!!
Answer:
Yes
Yes
No
No
Step-by-step explanation:
What is 2/3 of 9?
2
3
6
7
Answer: 6
Step-by-step explanation:
2/3 of 9 is basically 2/3 times 9
Answer:
6, because this and that is this and that bam boom bap, just trust me bro
Jacob's family takes the train to the city. The sign below shows information about the cost of train tickets. Jacob's family buys 2 adult tickets and 3 child tickets.
How much does it cost Jacob's family to take the train into the city?
Train Fare One-Way Adult $7 Child $6
It costs Jacob's family $
32
to take the train into the city.
You got it!
Jacob’s father pays for the tickets with $5 bills. He receives $3 in change. How many $5 bills does Jacob’s father use to pay for the tickets?
Answer:
it cost Jacob family $32 and he used 7 $5 bill to pay
Step-by-step explanation:
2 × 7 = 14
3 × 6 = 18
18 + 14 = 32
5x - 32 = 3
5x = 32 + 3
5x = 35
x = 35 ÷ 5
x = 7
A farmer is worried that a recent salmonella outbreak may have come from the carrots on his farm. He wants to test the carrots at the farm, but it will ruin the crop if he tests all of them.
a. If the farm has 10,000 carrots growing, describe a method that would
produce a random sample of 10 plants.
b. Why would a random sample be useful in this situation?
Answer: for b. Step-by-step explanation: The random sample would show multiple outcomes of the carrot growth and the combinations, i believe
LOOK AT THE PHOTO PLEASE
Answer:
The answer to the question provided is 4.
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \: 9x + 4 = 5x + 20 \\ \frac{ - 5x = - 5x}{4x + 4 = 20} \\ \frac{ \: \: \: \: \: \: \: \: - 4 = - 4}{ \frac{4x}{4} = \frac{16}{4} } \\ x = 4[/tex]
[I apologize if the answer to the question is inaccurate]