A person invested $7600 for 1 year, part at 6%, part at 9%, and the remainder at 13%. The total annual income from these investments was $818. The amount of money invested at 13% was $1200 more than the amounts invested at 6% and 9% combined. Find the amount invested at each rate.
Step-by-step explanation:
Let X be the amount invested at 6%, Y be the amount invested at 9%, and Z be the amount invested at 13%.
From the problem, we know that:
X + Y + Z = 7600 ---(1) (the total amount invested is $7600)
0.06X + 0.09Y + 0.13Z = 818 ---(2) (the total income from the investments is $818)
Z = X + Y + 1200 ---(3) (the amount invested at 13% is $1200 more than the amounts invested at 6% and 9% combined)
We can use equation (3) to substitute for Z in equations (1) and (2), then solve for X and Y as follows:
X + Y + (X + Y + 1200) = 7600
2X + 2Y = 6400
X + Y = 3200
0.06X + 0.09Y + 0.13(X + Y + 1200) = 818
0.06X + 0.09Y + 0.13X + 0.13Y + 156 = 818
0.19X + 0.22Y = 662
Using the system of equations X + Y = 3200 and 0.19X + 0.22Y = 662, we can solve for X and Y to get:
X = 800
Y = 2400
Substituting back into equation (3), we get:
Z = X + Y + 1200 = 4400
Therefore, the amounts invested at 6%, 9%, and 13% were $800, $2400, and $4400 respectively.
In January, the amount of snowfall was 5 2/3 feet. In February, the amount of snowfall was 3 1/5 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answer:
8 13/15
Step-by-step explanation:
Multiply the fractions so they both have the least common denominator:
5 2/3 = 5 10/15
3 1/5 = 3 3/15
Now, you can add the two mixed numbers:
[tex]5 \frac{10}{15} + 3 \frac{3}{15} = 8 \frac{13}{15}[/tex]
This is your final answer.
The length if a photograph is 6 inches less than twice the width. The photograph is mounted in a frame that is 3 inches wide on all sides. If the area of the framed picture is 270 square inches, find the dimensions of the unframed photograph.
Answer:
see below
Step-by-step explanation:
L = 2W-6
given: (L+3)*(W+3) = 270
so (2W-6+6)*(W+6) = 270
so 2W*(W+6) = 270
open up the brackets
2w²+12W = 270
so solve quadratic equations of 2w²+12W - 270 =0
w = 9 or -15
so dimensions of the unframed photograph = width 9, length 12
The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Approximately how many students received a
score between 70.5 and 80?
Answer:
B. 200 students
Step-by-step explanation:
Line t has equation y = -x - 2. Find the distance between l and the point D(-7, 0).
Round your answer to the nearest tenth.
the distance between line t and point D(-7, 0) is approximately 3.5 units.
what is distance ?
Distance is a measure of the amount of space between two objects or points. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can be either a scalar quantity
In the given question,
To find the distance between line t and point D(-7, 0), we need to first find the point on line t that is closest to point D.
We can use the formula for the distance between a point and a line in the coordinate plane:
distance = |Ax + By + C| / √(A^2 + B^2)
where Ax + By + C is the equation of the line in standard form, and (x, y) is the coordinates of the point.
In this case, the equation of line t is y = -x - 2, which we can rewrite in standard form as x + y + 2 = 0.
Using the formula above, we have:
distance = |x + y + 2| / √(1^2 + (-1)^2)
distance = |(-7) + 0 + 2| / √(2)
distance = 5 / √(2)
distance ≈ 3.5 (rounded to the nearest tenth)
Therefore, the distance between line t and point D(-7, 0) is approximately 3.5 units.
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Supplementary angles
Make a rap about why the kite is the best shape. Must be appropriate and at least 1 minute long. Giving brainless to whoever does it!!!!
Here is an attempt at an appropriately SFW 1 minute long rap about why the kite shape is the best:
The kite, soarin' high up in the sky,
Spreading colorful fabric far and wide.
There's no shape more perfect, this I must insist,
As it dances on the wind, ever blissful and lightly kissed.
Kite strings set it free, without any qualms,
Allowing it to float on high, away from harms.
Circling birds and beasts with graceful ease,
As a peaceful, wandering seas.
The kite shape is light but strong too,
Built to capture the breeze and soar true.
Diamond, square and box they can't compare,
To the kite so bright, beyond compare.
Many sizes to fit every quest,
From small pocket kites to giants they test.
Traditional or modern, simple or complex,
The kite is a form with many flexes.
Dragons and fighters, parafoils that stand,
On the beach or the park, across every land.
A kite for each mood and gusty seal,
As it dances and drifts from keel to keel.
So fly your kite up into the sun,
Some joyful moments, for now's the one.
Remember how free your kite did roam,
As a bird in the wind, and no longer alone.
The kite shape is art with physical grace,
Worth admiring for form, color and space.
There's magic up there among the open air,
As your kite soars high, beyond compare.
Here is an attempt at an appropriately SFW 1 minute long rap about why the kite shape is the best:
The kite, soarin' high up in the sky,
Spreading colorful fabric far and wide.
There's no shape more perfect, this I must insist,
As it dances on the wind, ever blissful and lightly kissed.
Kite strings set it free, without any qualms,
Allowing it to float on high, away from harms.
Circling birds and beasts with graceful ease,
As a peaceful, wandering seas.
The kite shape is light but strong too,
Built to capture the breeze and soar true.
Diamond, square and box they can't compare,
To the kite so bright, beyond compare.
Many sizes to fit every quest,
From small pocket kites to giants they test.
Traditional or modern, simple or complex,
The kite is a form with many flexes.
Dragons and fighters, parafoils that stand,
On the beach or the park, across every land.
A kite for each mood and gusty seal,
As it dances and drifts from keel to keel.
So fly your kite up into the sun,
Some joyful moments, for now's the one.
Remember how free your kite did roam,
As a bird in the wind, and no longer alone.
The kite shape is art with physical grace,
Worth admiring for form, color and space.
There's magic up there among the open air,
As your kite soars high, beyond compare.
if anyone understands this could u help me out???
Answer: V=1578.28 m³
Step-by-step explanation:
Volume is given as the formula
[tex]V=\frac{2}{3}\pi r^{3}[/tex]
r, radius, is the line from the center point to any end of the semi-sphere(that's what this shape is called) Here they show radius as
r=9.1
Substitute r into the formula
[tex]V=\frac{2}{3}\pi (9.1)^{3}[/tex] plug into calculator
V=1578.275 round to hundredths means 3 digits after the decimal point
V=1578.28 the number after the 7 is 5 or greater so you round up.
Wayne will toss a coin once and record eacthe toss as H for heads or T for tails.
Then he will randomly pick a card from a box that contains three cards numbered
1, 2, and 3, and he will record the number chosen. List all of the outcomes for the
event that the coin toss is tails.
Answer:
Step-by-step explanation:
The possible outcomes for the coin toss being tails and the card chosen being 1, 2, or 3 are:
-T1
-T2
-T3
Therefore, there are three possible outcomes for the event that the coin toss is tails.
Find the area of the following figure:
Answer: 61,6 in.
Step-by-step explanation:
To find the area of trapezoids with parallel bases, we add the length of the lower base to the length of the upper base.
[tex]12+10=22[/tex]Then we multiply this value by the height.
[tex](5.6).22=123.2[/tex]Finally, we divide the resulting value by [tex]2[/tex].
[tex]123.2/2=61.6[/tex]Evaluate the expression shown below and write your answer as a fraction. -5/9 -(-9/4)
Step-by-step explanation:
When we simplify the expression -5/9 - (-9/4), we can rewrite it as:
-5/9 + 9/4
To add these fractions, we need to find a common denominator. The least common multiple of 9 and 4 is 36, so we can convert both fractions to have a denominator of 36:
-5/9 = -20/36
9/4 = 81/36
Now we can substitute these values into our expression and add them:
-20/36 + 81/36 = 61/36
Therefore, the simplified expression is 61/36.
what’s answer
0.57
0.7
0.82
1.44
Answer:
Step-by-step explanation:
Sin O= opp/hyp
Sin 55 = BC/AB
Sin 55=.82
so
BC/AB=.82
Find the area of parallelogram WXYZ. Round your answer to the nearest tenth if
necessary.
21 in
18 in
21 in
23.2 in
23.2 in
Answer:
378in^2 i think
Step-by-step explanation:
In physical education class, students get one sticker for each mile they walk and two stickers for each mile they run. Jenny earned nine stickers
and completed seven miles. What would the graph look like?
The graph of the equation is linear
Given data ,
In physical education class, students get one sticker for each mile they walk and two stickers for each mile they run.
And , Jenny earned nine stickers
and completed seven miles
Based on the information provided, Jenny earned 9 stickers and completed 7 miles in physical education class. She receives one sticker for each mile she walks and two stickers for each mile she runs.
We can represent this information on a graph with the number of stickers earned on the vertical axis (y-axis) and the number of miles completed on the horizontal axis (x-axis).
Hence , the graph is solved
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15 postcards, 10 envelopes, and a notepad cost 1 dollar and 68 cents. The envelope is 8 times cheaper than the notepad and 2 cents more expensive than the postcard. What is the price of the postcard, the envelope, and the notepad?
Let's start by setting up some equations to represent the given information.
Let's say the price of a postcard is "x" cents.
Then, according to the problem statement, the price of an envelope is 8 times cheaper than the notepad, which means the price of an envelope is (1/8)th of the price of the notepad. So the price of an envelope is (1/8)*y cents, where "y" is the price of the notepad in cents.
Also, we know that the price of an envelope is 2 cents more expensive than the price of a postcard, so we can write:
(1/8)*y = x + 2 ...(Equation 1)
We also know that there are 15 postcards and 10 envelopes in the purchase, so the total cost of the postcards and envelopes is:
15x + 10[(1/8)*y] ...(Equation 2)
Finally, we have a notepad that costs "y" cents. So the total cost of the purchase is:
15x + 10[(1/8)*y] + y ...(Equation 3)
We are given that the total cost of the purchase is 1 dollar and 68 cents, which is equal to 168 cents. So we can write:
15x + 10[(1/8)*y] + y = 168 ...(Equation 4)
Now we have four equations (Equation 1, Equation 2, Equation 3, and Equation 4) with three variables (x, y, and 168). We can solve for x and y by using a system of equations.
From Equation 1, we can solve for y in terms of x:
(1/8)*y = x + 2
y = 8x + 16
Substituting this expression for y into Equations 2 and 3, we get:
15x + 10[(1/8)*y] = 15x + 10(8x + 16) = 160x + 160
15x + 10[(1/8)*y] + y = 15x + 8x + 16 = 23x + 16
Substituting these expressions into Equation 4, we get:
23x + 16 = 168
Solving for x, we get:
x = 6
Substituting this value for x into Equation 1, we can solve for y:
(1/8)*y = x + 2 = 6 + 2 = 8
y = 64
So the price of a postcard is 6 cents, the price of an envelope is (1/8)*64 + 2 = 10 cents, and the price of a notepad is 64 cents
NO LINKS!!! URGENT HELP PLEASE!!
Edward opens a savings account with $250. The bank gives him an interest rate of 2.8% per year (simple interest). About how long will it take Edward to double his money? (SHOW WORK!!)
Equation: ___________________
Answer: __________________
Answer:
Equation: 250(1 + 0.028t) = 500
Answer: 36 years
Step-by-step explanation:
The equation we can use to solve this problem is the simple interest formula:
[tex]\boxed{A = P (1 + rt)}[/tex]
where:
A is the amount of money in the account after t years.P is the principal (initial amount).r is the interest rate per year (as a decimal).t is the time in years.Given the initial investment is $250 at an interest rate of 2.8%, and Edward wants to double his money:
A = $500P = $250r = 0.028Substite these values into the equation:
[tex]500=250(1+0.028t)[/tex]
Swap sides:
[tex]250(1+0.028t)=500[/tex]
Now solve for t:
[tex]\implies \dfrac{250(1+0.028t)}{250}=\dfrac{500}{250}[/tex]
[tex]\implies 1+0.028t=2[/tex]
[tex]\implies 1+0.028t-1=2-1[/tex]
[tex]\implies 0.028t=1[/tex]
[tex]\implies \dfrac{0.028t}{0.028}=\dfrac{1}{0.028}[/tex]
[tex]\implies t=35.71428571...[/tex]
Assuming the interest is applied annually on the anniversary of the account opening, it will take Edward 36 years to double his money with a 2.8% simple interest rate.
A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot.
A wine producer in California, where merlot is produced, believes the figure is higher in California. She
contacts a random sample of 550 California residents and asks which wine they purchase most often.
Suppose 115 replied that merlot was the primary wine.
(a) Calculate the appropriate test statistic to test the hypotheses.
(b) Calculate the p-value associated with the test statistic, and test the claim at α = 0.01.
The sample data provides sufficient evidence to conclude that the population proportion is greater than 0.17 at 1% level of significance.
What is a Null Hypothesis?
One can define a null hypothesis as a declaration that postulates no noteworthy variance or association between two or more variables existing within a populace.
Usually utilized in statistical hypothesis testing, it evaluates if an observed effect or relation is statistically meaningful or arises purely by chance.
It often bears the insignia H0 and subject to an alternative proposition (Ha) signifying a significant outcome or connection instead. Whenever the null hypothesis gets dismissed, one may deduce that there are ample findings to sustain the alternate assertion's validity.
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A landscape architect is designing a pool that has this top view. How much water will be needed to fill this pool 4 feet deep?
The amount(volume) of water that will be needed to fill the pool is 144 ft³.
What is volume?Volume is the space occupied by a solid shape.
To calculate the amount(volume) of water that will be needed to fill the pool, we use the formula below
Formula:
V = H(LW-l²)........................ Equation 1Where:
V = Volume of the water needed to fill the poolH = Height of the poolFrom the diagram in the question,
Given:
H = 4 ftL = 8 ftW = 5 ftl = 2 ftSubstitute these values into equation 1
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Solve for the length of the missing side in the triangle. Leave your answer in radical form. Show your work and
explain the steps you used to solve.
17
The length of the missing side is given as follows:
[tex]x = \sqrt{155}[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For the triangle in this problem, the sides and the hypotenuse are given as follows:
Sides of 13 and x.Hypotenuse of 18.Hence the missing side is given as follows:
x² + 13² = 18²
x = sqrt(18² - 13²)
x = sqrt(155) -> most simple radical form.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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Find the measures of angle BED
keeping in mind that twin sides make twin angles, Check the picture below.
Carmine takes a loan for $11,500 at a rate of 8% that is compounded quarterly. Assuming she makes no payments for the first 2 years, what is her loan balance?
Carmine's loan balance after two years would be approximately $13,827.72.
Define the term loan?In mathematics, the term "loan" typically refers to a sum of money that is borrowed by one party from another with the agreement to repay it with interest over time. Loans are a common financial concept used in various areas of mathematics, such as finance, economics, and business.
What does compounded quarterly means?"Compounded quarterly" refers to a method of calculating interest or investment growth where the interest is added to the principal and then reinvested or recalculated at the end of each quarter (every three months) within a given time period.
To calculate Carmine's loan balance after two years, we need to use the compound interest formula, which is given by:
A = P ×[tex](1+r/n)^{nt}[/tex]
Where:
A = the loan balance after t years
P = the initial principal amount (loan amount) = $11,500
r = annual interest rate = 8% or 0.08 (expressed as a decimal)
n = number of times interest is compounded per year = 4 (since it is compounded quarterly)
t = time in years = 2 (since Carmine made no payments for the first two years)
Putting the values into the formula, we get:
A = 11,500 × (1 + 0.08/4)⁸
A = 11,500 × (1 + 0.02)⁸
A = 11,500 × (1.02)⁸
A ≈ $13,827.72
So, Carmine's loan balance after two years would be approximately $13,827.72.
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PLEASE HELP WILL GIVE BRAINLEST FOR CORRECT ANSWER ONLY !!
(Enlarge photo)
The answer is D :) )
Write the following number in standard decimal form. one and ninety-six ten-thousandths 0 X
What is the concentration of H+ ions at a pH = 7?
mol/L
What is the concentration of OH-ions at a pH=7?
mol/L
What is the ratio of H* ions to OH-ions at a pH = 7?
:1
The concentration of H⁺ ions at a pH of 7 is 1 x 10⁻⁷ M.
What is the concentration of the ion?Ion concentration refers to the amount of ions that are present in a solution or a medium, expressed in terms of their concentration.
The concentration of ion with pH of 7 is calculated as follows;
pH = -log[H⁺]
[H⁺] = 10^(-pH)
The given pH = 7, so the ion concentration is calculated as;
[H⁺] = 10⁻⁷
[H⁺] = 1 x 10⁻⁷ M
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What is the area of a right triangle with a height of 6 1/4 yards and base of 22 yards
Answer:
The area should be 0.5 * b * h
Step-by-step explanation:
B stands for the base of the triangle and H is the height
A point moves along a curve y=2x^2 + 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x= 3/2?
If the "y-value" is decreasing at rate of 2 units per second, the rate at which "x" is changing when x=3/2 is -1/3 units per second.
The point moves along a curve having equation as : y = 2x² + 1; and
We know that y is decreasing at a rate of 2 units per second. We have to find the rate at which "x" is changing when x = 3/2,
To solve this problem, we differentiate, the curve equation,
So, taking the derivative of both sides of the equation with respect to time "t",
We get,
⇒ d/dt (y) = d/dt (2x² + 1),
⇒ dy/dt = (4x) × dx/dt,
We are given that dy/dt = -2 (since y is decreasing at a rate of 2 units per second), and we need to find "dx/dt" when x = 3/2,
Substituting "x = 3/2" and "dy/dt = -2",
We get,
⇒ -2 = 4×(3/2)(dx/dt),
⇒ -2 = (6)×(dx/dt),
⇒ dx/dt = -1/3,
Therefore, the rate at which "x" is changing when x = 3/2 is -1/3 units per second.
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The given question is incomplete, the complete question is
A point moves along a curve y=2x² + 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x= 3/2 ?
it takes 2/3 of a gallon of paint to cover 3/4 of a wall. How many gallons of paint are needed to cover a full wall?
how do i find the area of this shape?
Answer:
(1/2)(12)(16) + (1/2)π(6^2)
= (96 + 18π) square cm
= about 152.55 square cm
y = -x + 10 y = -x + 12
The solution to the given simultaneous equation y = -x + 10 ; y = -x + 12 is zero.
How to solve simultaneous equation?
y = -x + 10
y = -x + 12
Subtract both equations
y - y = -x -(-x) + 10 -12
0 = -x + x - 2
0 = 0 - 2
0 = -2
In conclusion, zero is the solution to the equation
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Can someone please help me
The height of the Ferris wheel at point A is 100 ft.
The height of the Ferris wheel at point B is 182.1 ft.
The height of the Ferris wheel at point C is 39.9 ft.
What is the height of the Ferris wheel at each point?
The height of the Ferris wheel at each point is calculated as follows;
The height of a point on a circle; H = h + y
Where;
h is the height of the center of the circley is the vertical component of the point's position vectorH = h + rsinθ
where;
r is the radius of the circle.θ is the angle of rotationFor point A with θ = 0 radians;
H = 100 + 85 x sin (0)
H = 100 ft
For point B with θ = 7π/12 radians;
H = 100 + 85 x sin(7π/12)
H = 182.1 ft
For point C with θ = 5π/4 radians;
H = 100 + 85 x sin(5π/4)
H = 39.9 ft
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