A financial instrument pays 8% simple interest (based on the purchase value) and matures after 3 years. The instrument can be purchased at any price.
An investor purchases the instrument for P dollars, and calculated that the total value of the investment (i.e. P plus interest earned) will be $2,000 at maturity. Calculate P.
we know it pays using simple interest.
So the investor bought it a P dollars, maturity time is 3 years, namely t = 3, rate is 8% or namely r = 8/100, and it'll yield 2000, or A = 2000, let's plug those in the simple interest earned amount equation.
\(~~~~~~ \textit{Simple Interest Earned Amount}\\\\A=P(1+rt)\qquad\begin{cases}A=\textit{accumulated amount}&\dotfill \$2000\\P=\textit{original amount deposited}\\r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\\stackrel{maturity}{t=years}\dotfill &3\end{cases}\\\\\\2000=P(1+0.08\cdot 3)\implies \cfrac{2000}{1+0.08\cdot 3}=P\\\\\\ \cfrac{2000}{1.24}=P\implies \boxed{1612.90 \approx P}\)
The required amount for the initial investment is given as P = $1613.
As mentioned in the question, a financial instrument pays 8% simple interest (based on the purchase value) and matures after 3 years. The instrument can be purchased at any price.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Here,
Amount = principal + simple interest,
Amount = p + prt /100
Amount = p(1 + rt /100)
Substitute the values,
2000 = p (1 + 8× 3 / 100)
2000 = p[124/100]
p = 1612.90 ≈ $1613
Thus, the required amount for the initial investment is given as P = $1613.
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Avery's recipe ask for 100ml of milk. She only has a 10ml measuring cup. How many times will she need to fill her measuring cup to get the right amount of milk for her recipe
Ten times to get the required amount of 100ml of milk for her recipe.
Avery needs to measure 100ml of milk for her recipe but she only has a 10ml measuring cup.
Therefore, she needs to determine how many times she will need to fill her 10ml measuring cup to get the required amount of milk.
To calculate this, we can divide the required amount of milk by the capacity of the measuring cup. In this case, we divide 100ml by 10ml to get:
100ml ÷ 10ml = 10
This means that A very will need to fill her 10ml measuring cup 10 times to get the required amount of milk for her recipe.
Another way to think about it is to consider that 100ml is ten times the capacity of the 10ml measuring cup. Therefore, Avery will need to fill the measuring cup ten times to get the required amount of milk.
In summary, Avery will need to fill her 10ml measuring cup ten times to get the required amount of 100ml of milk for her recipe. t
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Mr. Dominguez invests $3,000 in a savings plan. The savings account pays an annual interest rate of 4.2% on the amount he put in at the end of each year. Create (and label) a graph in the coordinate plane to show the relationship between time and the amount of interest earned for the first 5 years of the investment. Is the relationship proportional? Why or why not? If so, what is the constant of proportionality?
Answer:
is 5 point worth it ummm no
Step-by-step explanation:
How many edges does the following shape have?
Answer:
6
Step-by-step explanation:
easy middle school math problem
Find the measures of angle x and angle y
the 2 angles are equal so both are 148
Could you please help me on this question out really appreciate it!
6. Find the area of the shaded region.
sm
5 m
7 m
8 m
A. O 56 square meters
B. O 12.5 square meters
C. O 40 square meters
D.O 23 square meters
moyolaliste
SO
Answer:
B. 12.5 square meters
Step-by-step explanation:
The bottom side is 5, because the length of the longer side is 8, and the shorter side is 3, so 8-3=5. The height of the triangle is 5. Use the area formula of a triangle: 1/2*base*height, and you get 1/2*5*5. 1/2 of 5 is 2.5, 2.5 times 5 iss 12.5
The graphs below have the same shape. Complete the equation of the redgraph. Enter exponents using the caret (-); for example, enter A as x^4. Donot include "G(x) ="
We can see that the graph of F(x) was moved 2 units up to get the graph of G(x). Adding 2 units to F(x) we have:
G(x) = 3 - x^4 + 2
G(x) = 5 - x^4
The answer is 5 - x^4
A square room is extended so that it is 2.5m wider and 3.7m longer. If it's ne2 area is 54.4m². Find it's original length and width.
If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of
60 km. How far will it travel if it continues this average rate for 4 hours? (answer in
meters)
Answer:
240,000 Meters
Step-by-step explanation:
if your going 60 km/h and you drive at that speed for 4 hours that equals 240 km you have driven now to convert to meters there is 1000 meters in 1km so 240 x 1000 is 240,000
Answer:Non
Step-by-step explanation: is what the energy of you did to
As the standard deviation (σ) decreases, the width of the confidence interval _______________.
Answer:
increases
Step-by-step explanation:
The width of the confidence interval decreases as the sample size increases.
When there is the decrease in the standard deviation so the width of the confidential interval should be increased.
Given that,
There is the decrease in the standard deviation. We have to know the status of the confidence interval width.Based on the above information, the following information should be considered.
When the confidence interval width should be decreased because there is an increase in the sample size. Also, there is an inverse relationship between both of them.Therefore we can conclude that when there is the decrease in the standard deviation so the width of the confidential interval should be increased.
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Determine the domain of the function F(x) =2-x/12x^2+8x
For safety reasons, the angle a ladder makes with the ground should be no greater than 67°. Find the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high.
Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.
What are trigonometric functions?
Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the angle a ladder makes with the ground should be no greater than 67°.
So the angle θ ≤ 67°.
Let us assume the angle to be equal to 67°
The height of the roof from the ground is 23 feet.
The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.
With the sine function, find the length of the ladder -
sin θ = perpendicular/hypotenuse
Let the length of ladder be x.
sin 67° = 23/x
x = 23/sin 67°
x = 23/0.920
x = 25 feet
Therefore, the length of the ladder is 25 feet.
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-26 =3v +1 can i please get a answer
Step-by-step explanation:
-26=3v+1
-1 on both sides
-27=3v
divide by 3 both sides
-9=v
solve
emergency , please i need your help or i might get detention
Answer:
Answer is 2
Step-by-step explanation:
To get rid of the fraction:
5*4x-5 =3
5
4x-5=3
4x=3+5
4x=8
x=2
Step-by-step explanation:
It should be 5x4= 20
-5=15
15÷5
=3
the sum of two consecutive odd integers is less than four times the smaller of two integers. What is the value of each integer
Consecutive odd integers differ by 2. For example, 1, 3, 5, 7. The difference is 2
Let x represent the smaller odd integer. This means that the larger consecutive integer is x + 2
From the information given, the sum of two consecutive odd integers is less than four times the smaller of two integers. it means that
\(\begin{gathered} x\text{ + x + 2 }<4\times x \\ 2x\text{ + 2 }<4x \\ 2\text{ }<4x\text{ - 2x} \\ 2<\text{ 2x} \\ \text{Dividing both sides by 2, } \\ 1\text{ < x} \\ x\text{ > 1} \end{gathered}\)The value of the smaller integer ranges from 2 to infinity. Since 2 is not odd, it starts from 3
The value of the larger integer ranges from 3 + 2 to infinity. Therefore,
The value of the larger integer ranges from 5 to infinity
Select all lengths that are equal to 3 yards 16 inches.
The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).
To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.
1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).
Therefore, 3 yards is equal to 3 * 36 = 108 inches.
Now, we can compare 108 inches to 3 yards 16 inches.
108 inches is equal to 3 yards, so it matches the given length.
To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.
Therefore, 3 yards 16 inches is equivalent to:
3 yards
108 inches
3 yards 0.44 yards (or approximately 3.44 yards)
108 inches 0.44 yards (or approximately 108.44 inches)
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Solve for x leave your answer in simplest radical form
Answer:
X=11 trust me on my mom
Sketch the graphs. - 2x + 3y = -1
Answer:
Step-by-step explanation:
y =2/3x + 1/3
slope 2/3
y-intercept: (0 ,1/ 3)
Answer:
Step-by-step explanation:
- 2x + 3y = -1 is the equation of a line
Pick any values for x then find y or for y and then find x;
if you have two points you can draw a line trough those two points.
For example,
pick x= -1 then find y
- 2*(-1) + 3y = -1
2+ 3y = -1
3y = -1-2
y= -3/3
y= -1
First point has the coordinates (-1, -1)
pick y = 1 then find x
- 2x + 3*1 = -1
-2x +3 = -1
-2x = -1-3
-2x = -4
x= -4/-2
x= 2
Second point has the coordinate (2, 1)
Draw a line trough the points (-1, -1) and (2,1) to sketch the graph of -2x+3y = -1
Find the exact value of cos A in simplest radical form.
Round your answer to the nearest cent.
Answer:
Brand A: $0.05
Brand B: $0.07
Brand A is the better buy
Step-by-step explanation:
Brand A: 72x = 3.89
Brand B: 96x = 6.62
Brand A:
72x = 3.89
/72 /72
x = $0.05 (this one is the better buy)
Brand B:
96x = 6.62
/96 /96
x = $0.07
Hope this helps!
Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
Looking at the table above ,
A. What would you consider as the independent variable in this situation ? Introduce the symbol/ name (x,t,...) you will use to represent this variable . Remember to include the units.
B. What is the dependent variable ? Introduce the symbol /name for this variable . Remember the units .
The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).
The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.
The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.
The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.
An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.
In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).
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Please help I am so so confused thank you all
y-(-9) = -6(x-(-4)), y = -6x-33
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
Factorise:- y^3+1+2y^2+2y
Step-by-step explanation:
Given equation, 2x
3
+3x
2
+3x+1=0
⟹2x
3
+2x
2
+x
2
+2x+x+1=0⟹(2x+1)(x
2
+x+1)=0
Solving the 2 equations, we have x=
2
−1
,
2
−1±
3
i
Answer:
y( y^2+1+2y+2)
Step-by-step explanation:
taking common of all
Please help, thanks!
What is the value of x? 1/6 (3 - 2x) < 1/3 x
Step-by-step explanation:
1/6 (3 - 2x) < 1/3 x
let's multiply everything by 6
3 - 2x < 6/3 x
3 - 2x < 2x
3 < 4x
3/4 < x
so, x > 3/4
since 3/4 is never equal to x but is purely smaller than x, the interval of valid x values starts right after 3/4 and goes to infinity.
x = 3/4 is not valid, because 3/4 is not smaller than 3/4 (it is equal to) ...
please help soon!! will award brainliest
three shapes. three areas to find. three areas to add together to find the whole area. gotcha.
Step-by-step explanation:
smaller rectanglelarger rectangleright trianglesmaller rectangle:
length is 7 cm and width is 4 cm, so the area is 28 square cm
larger rectangle:width is 4 cm and length is 10 cm, so the area is 40 square cm
Because the weird shape's bottom length was 13 cm. There are 3 cm and 7 cm on the top length(s) of the weird shape, next to each other. Looking at the dash lines, when adding 3 cm and 7 cm together, the larger rectangle's length is 10 cm.
right triangle:base is 3 cm and height is 8 cm, so the area is (3x8)/2 = 24/2 = 12 square cm
With knowledge from figuring out the larger rectangle's length being 10 cm and the weird shape's bottom length being 13 cm, we know the right triangle's base is 3 cm. (13 cm - 10 cm = 3 cm for the base of the right triangle).
Due to adding 4 cm and 4 cm of weird shape's width, which is also a right triangle's height.
weird shape's area from adding three shapes' areas:28 + 40 + 12
= 80 square cm (ANSWER)