A mother wants to invest $13000 for her children's education. She invests a portion of
the money in a bank certificate of deposit (CD account) which earns 4% and the
remainder in a savings bond that earns 7%. If the total interest earned after one year is
$780, how much money was invested at each rate?
Answers
The amount invested at 4% is $4,333.33
The amount invested at 7% is $8,666.67
What represents the amount invested at 4%?
Let assume that x is the amount invested in the bank certificate of deposit (CD account) which earns 4%, in essence, the interest earned at 4% is the amount of money invested multiplied by 4%
interest at 4%=4%*x=0.04x
amount invested at 7%=13000-x
interest at 7%=7%*(13000-x)
interest at 7%=910-0.07x
total interest=0.04x+910-0.07x
total interest=910-0.03x
total interest earned=780
780=910-0.03x
0.03x=910-780
0.03x=130
x=130/0.03
x=amount invested at 4%=$4,333.33
amount invested at 7%=$13,000-$4,333.33
amount invested at 7%=$8,666.67
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Related Questions
In each diagram, line f is parallel to line g, and line t intersects lines f and g
Answers
In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.
Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.
Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.
Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.
Alternate interior angles are congruent, as well as alternate exterior angles.
By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.
It is important to measure angles systematically and compare them to find congruent or equal measures.
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13. Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point?
14. To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
15. A suitcase measures 24 inches long and the diagonal is 30 inches long.
How much material is needed to cover one side of the suitcase?
Answers
The solution is : 22 meters would be saved if it were possible to walk through the pond.
Here, we have,
There is a pond between two points A and B.
To avoid the pond, one must walk to the south from point A to point C (say) by 34 meters and then to the east from point C to point B by 41 meters.
Now, it is clear that Δ ABC is a right triangle with AB as the hypotenuse that is the minimum distance from A to B through the pond.
The two legs of the right triangle are AC and CB.
Applying Pythagoras Theorem,
AB² = AC² + CB²
= 34² + 41²
= 2837
⇒ AB = 53 meters (Rounded to the nearest meter)
Therefore, (34 + 41) - 53 = 22 meters will be saved if it were possible to walk through the pond.
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complete question:
To get from point A to point B you must avoid walking through a pond. To
avoid the pond, you must walk 34 meters south and 41 meters east. To the
nearest meter, how many meters would be saved if it were possible to walk
through the pond?
how to write 3 over 8 as a power
Answers
Answer:
(3/8 )^1
Step-by-step explanation:
that's the only way, unless you want to get into logs, on that case, we can set the equation as 3/8 = x^y
from here we take log y both sides and get
logy(3/8) = x
and here we get 3/8 = y^x
solving this we see that x^y = y^x
we know that y has to equal 0 or 1 or x equals 0 or 1
but neither can equal 0, so y has to equal 1 and x equals 3/8 :)
Which ordered pairs are solutions to the system of inequalities?
More than one answer
y ≥ x + 2
y > -5/2x - 3.
A. (0,0)
B. (-2,2)
C. (0,2)
D. (-1,6)
Answers
Answer:
C, D
Step-by-step explanation:
We can solve this graphically and analytically.
Graphically, looking at the attached image below, if we graph the two inequalities and plot the points, you can find the points which are solutions by finding the points in the overlapping area.
This obviously excludes A as it only appears in \(y \geq x+2\)
C is included as y \(\geq x+2\) includes the point on the line.
D is obviously a solution.
B is however not a solution because is lies on the line \(y = \frac{-5x}{2} - 3\), which the inequality excludes.
Analytically, if we can find one of the two inequalities where it is not a solution, it is not a solution of the system.
A: (0, 0)
\(y \geq x+2\\0 \geq 0 + 2\\0 \geq 2\\false\)
A is not a solution
B: (-2, 2)
\(y \geq x+2\\2 \geq -2 + 2\\2\geq 0\\true\)
\(y > \frac{-5x}{2} -3\\2 > \frac{-5(-2)}{2} - 3\\2 > 5 - 3\\2 > 2\\false\)
B is not a solution
C: (0, 2)
\(y \geq x+2\\2 \geq 0 + 2\\2 \geq 2\\true\\\\y>\frac{-5x}{2}-3\\2 > -3\\true\)
C is a solution
D:
\(y \geq x + 2\\6 \geq -1 + 2\\6 \geq 1\\true\\\\y > \frac{-5x}{2} - 3\\6 > \frac{-5(-1)}{2} - 3\\6 > \frac{5}{2} - \frac{6}{2}\\6 > \frac{-1}{2}\\true\)
D is a solution
A company has determined that its maximum profit occurs when it sells 10,000units per month. For every 1,000 units more or less than 10,000 units that thecompany sells, its profit decreases by $5,000. Which of the following equationscan be used to find the number of units, q, in thousands, for which the profitdecreases $35,000 from the maximum?
A. 10 |q−35| =5
B. 5 |q−10| =35
C. 35 |q−10| =5
D. 5 |q−35| =10
Answers
Answer:
B. 5 |q−10| =35
Step-by-step explanation:
Solution:
let's try to understand the problem clearly.
In this question, we asked to calculate the number units which that company produces so that it's profit is decreased from the maximum profit.
We know that, for 10000 units = company will get maximum profit.
Any value less than or greater than 10000 units will decrease the profit.
and we also know that,
For every 1000 units profit is decreased by $5000.
So if maximum profit is at 10000 units,
Then at 9000 units = it will have profit decreased by 5000 from the maximum
if q = 11000 then profit = Maximum - 5000
But we are asked to calculate the profit decrease of $35000 from the maximum.
it means we need 5000 decreased by 7 times = 10000 + 7000 = 17000 units
So, if company produces 17000 units,
profit will be decreased by 5(7000) = 35000
Finally,
B. is the only equation which satisfies this condition.
B. 5 (q-10) = 35
(q-10) = 7
q = 10 + 7 = 17
q = 17000 units
Hence, for 17000 units, company's profit will decrease $35000 from the maximum profit.
Find the average rate of change of the function below over the interval (-4,-1).
Answers
Answer:
-2
Step-by-step explanation:
\(\frac{f(b)-f(a)}{b-a}\\ \\=\frac{f(-1)-f(-4)}{-1-(-4)}\\ \\=\frac{-4-2}{-1+4}\\ \\=\frac{-6}{3}\\ \\=-2\)
Therefore, the average rate of change over the interval [-4,-1] is -2.
Based on the graph how many bottles will be filled in 80 seconds? 
Answers
Answer:
Below
Step-by-step explanation:
Find unit rate (since it starts at 0,0)
at 45 seconds it is 900 bottles
900 bottles / 45 seconds = 20 bottle / sec
20 bottles / sec * 80 sec = 1600 bottles
I need help asap. PLs
Answers
The height of the trapezium is approximately 7.898 ft.
Describe Trapezium?A trapezium (also called trapezoid in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezium.
There are different types of trapeziums, such as isosceles trapeziums, where the legs are equal in length, and right trapeziums, where one of the angles formed by a base and a leg is a right angle.
The area of a trapezium is given by the formula:
Area = (1/2) × (sum of bases) × height
where the sum of bases is the sum of the lengths of the two parallel sides.
The perimeter of a trapezium is given by the sum of the lengths of all four sides:
Perimeter = length of base 1 + length of base 2 + length of leg 1 + length of leg 2
We can use the formula for the area of a trapezium to solve for its height. The formula is:
Area = (1/2) x (sum of parallel sides) x (height)
We are given the area of the trapezium as 79.395 ft, the length of one of the parallel sides (the base) as 15.1 ft, and the length of the other parallel side as 5 ft. Let's plug these values into the formula and solve for the height:
79.395 = (1/2) x (15.1 + 5) x h
79.395 = 10.05h
h = 79.395 / 10.05
h = 7.898 ft (rounded to three decimal places)
Therefore, the height of the trapezium is approximately 7.898 ft.
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you use a line of best fit for a set of data to make a prediction about an unknown value
Answers
A straightforward linear regression study of two or more independent variables will provide a straight line. A curved line may occasionally result from a multiple regression involving a number of linked variables.
What is line of best fit?
The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. The geometric equation for the line is often calculated manually or using software using the least squares approach, also referred to as ordinary least squares, or OLS.
A straight line that minimizes the gap between it and some data is called a line of best fit.In a scatter plot containing various data points, a relationship is expressed using the line of best fit.It is a result of regression analysis and a tool for forecasting indicators and price changes.The line of best fit is a tool used in finance to find patterns or correlationsTo learn more about regression line, click on below link:
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Katie's earnings, E , for a week are given by the equation E = 18h, where H is the number of hours that Katie works during the week. If Katie works 40 hours per week for 4 weeks, how much money will she earn during the 4-week period?
Answers
Answer:
$2,880
Step-by-step explanation:
18 x 40 = 720 earned per week
720 x 4 (weeks) = 2880 earned in 4 weeks
A news agent conducted a survey of business magazine subscribers in a town and found that there was
circulation of only three business magazines. He made the Venn diagram below to show the number of
subscribers to each of the three magazines: Board Review, Strategy and Finance, and Investor Journal
Answers
394 subscribers are represented in the venn diagram.
What is venn diagram?Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.
Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.
according to the venn diagram
196+41+21+52+84 = 394
There are 394 subscribers
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45 x 6 = 6 x 45 what multiplication property
Answers
Answer:
commutative property of multiplication
Step-by-step explanation:
doesnt matter 2*1 or 1*2 you will get the same answer
The perimeter of this shape is 29 cm.
What the value of x?
Answers
Answer:
X=7
Step-by-step explanation:
So first add them all up
x-2+2x+x+3=4x+1
4x+1=29
4x=28
x=7
Find the vertex, focus, and directrix of the parabola.(y + 3)^2 = 16(x - 3)
Answers
We will have the following:
We are given the parabola:
\((y+3)^2=16(x-3)\)And we can see that it follows:
\((y-k)^2=4p(x-h)\)Now, we will have that the vertex is given by:
\((h,k)\)From the equation we then have that the vertex is:
\((3,-3)\)Now, we can see that p = 4 since 16 / 4 = 4. Now, we remember that the focus is located p units to the right since it is positive, thus the focus is given by:
\((h+p,k)\)So, the focus is at:
\((3+4,-3)\to(7,-3)\)Finally we will have that the directrix of the parabola will be given by:
*First, we find the distance between the focus and the vertex, that is:
\(d=\sqrt[]{(7-3)^2+(-3-(-3))^2}\Rightarrow d=4\)Now, since the x coordinate of the vertex is 3, then the directrix will pass at 4 units to its left, that is the directrix is given by:
\(x=-1\)That can be seing in the graph:
*** Summary***
Vertex: (3, -3)
Focus: (7, -3)
Directrix: x = -1
) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answers
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
Given MB = PB and m arc PB = 27°, find the m∠PBM
Answers
The measure of the angle m∠PBM is calculated as; 54°
How to find the measure of the interior angle of an arc?An inscribed angle is defined as an angle with its vertex on the circle.
The measure of an inscribed angle is half the measure the intercepted arc.
The formula is:
Measure of inscribed angle = 1/2 × measure of intercepted arc
Now, we are given that;
MB = PB
Arc PB = 27°
Thus;
Arc MBP = 2 * 27°
Arc MBP = 54°
Thus, using the Measure of inscribed angle we have;
∠PBM = 27 * 2 = 54°
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When csc(Theta)sin(Theta) is simplified, what is the result? StartFraction 1 Over cosecant squared EndFraction StartFraction 1 Over sine squared EndFraction 0 1
Answers
Step-by-step explanation:
csc θ sin θ
(1 / sin θ) sin θ
1
The simplified value of the given expression comes to be 1.
The given expression is:
\(cosec\theta.sin\theta\)
What is the trigonometric ratio \(cosec\theta\)?The trigonometric ratio \(cosec\theta\) is the ratio of the hypotenuse to the opposite side. It is the inverse of \(sin\theta\).
\(cosec\theta=\frac{1}{sin\theta}\)
We know that \(cosec\theta=\frac{1}{sin\theta}\)
So \(cosec\theta.sin\theta\)
\(=\frac{1}{sin\theta} .sin\theta\)
=1
So, the simplified value is 1.
Hence, the simplified value of the given expression comes to be 1.
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For a floral arrangement class, Jayvon has to create an arrangement of twigs and flowers that has a total of 9 objects. Jayvon has to pay for the twigs and flowers that he uses in his arrangement. Each twig costs $1, and each flower costs $3. He spends a total of $15 on the twigs and flowers. Write and solve a linear system to find the number of twigs and the number of flowers he used. Use the method of substitution.
Answers
Answer:
3 flowers 6 twigs
Step-by-step explanation:
set flowers to x and twigs to y
15 = 3x + y subtract 3x both sides to get y
9 = x+y sub 15-3x in for y 9= x + 15-3x simplify to 2x =6 so x =3 put that in for x in 9=x+y 9= 3+ y so y =6
This system of equations is:This system of equations is:This system of equations is:consistent dependentconsistent independentinconsistentconsistent dependentconsistent independentinconsistentconsistent dependentconsistent independentinconsistentThis means the system has:This means the system has:This means the system has:a unique solutionSolution: 00a unique solutionSolution: 0.0O a unique solutionSolution: 0.0no solutioninfinitely many solutionsno solutioninfinitely many solutionsno solutioninfinitely many solutions
Answers
I WILL GIVE 5 STARS AND LIKE PLEASE RESPOND WITH ACTUAL ANSWER
Account A has a simple annual interest rate of 2% and Account B has a simple annual interest rate of 2.5%. How much more interest do you earn per year when you deposit X dollars in Account B instead of Account A?
Answers
Answer:
Ok nice and easy, you earn about 0.04% more interest
Step-by-step explanation:
So lets do an easy number 100 for example.
100(0.2) = 2 2+100=102 102 is for A
100(0.025) = 2.5 100+2.5=102.5 102.5 is for B
Find the percentage change
new-old/old
102.5-102=0.5
0.5/102= 0.0043 (infinity)
Round it to a percent and the nearest percent
0.04%
We can do a check with a different number
1000(0.2)= 20 20+1000=1020
1000( 0.025)= 25 25+1000= 1025
find the percentage change
1025-1020=5
5/125= 1/25
1/25= 0.04
so there you go :)
Simplify the expression 5x2+6x+4+x2+x
.
Thank You!
Answers
The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
The given expression is 5x²+6x+4+x²+x
Simplifying the given expression
5x²+6x+4+x²+x
Firstly, put the similar terms together
5x²+x²+6x+x+4
Adding the similar terms
6x²+7x+4
∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.
Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
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the wheel of a bike has a diameter of 27 inches. find the circumference of the wheel.
Answers
The circumference of the wheel of the bike given the diameter is 84.78 inches
What is the circumference of the wheel?As evident from the task content; it is required that the circumference of the bike's wheel be determined.
Given that the Diameter of the wheel = 27 inches
Recall; Radius = diameter / 2
= 27/2
= 13.5 inches
π = 3.14
Since the formula for the Circumference of the wheel which is circular = 2πr
= 2 × 3.14 × 13.5
= 84.78 inches
In conclusion, the circumference of the wheel according to the given description is 84.78 inches.
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PLS HURRY AND ANSWER I NEED THE ANSWER!!!! PLS
An icecream machine can make 6 quarts in 8 hours. At this rate, how
many quarts can it make in 64 hours?
A.
42
B.
36
C.
24
D.
48
Answers
Answer:
48 i think
Step-by-step explanation:
im not 100% persint sure
g(x)=-x-1 find g(-4)
Answers
Answer:
g(-4) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = -x - 1
g(-4) is x = -4
Step 2: Evaluate
Substitute in x: g(-4) = -(-4) - 1Multiply: g(-4) = 4 - 1Subtract: g(-4) = 3A prime number is a number that is evenly divisible only by 1 and itself. The prime numbers less than 100 are listed below.2 3 5 7 11 13 17 19 23 29 3137 41 43 47 53 59 61 67 71 73 7983 89 97Choose one of these numbers at random. Find the probability thata. The number is odd b. The sum of the digits is odd c. The number is greater than 70
Answers
Answer:
a. 0.96 = 96% probability that the number is odd.
b. 0.48 = 48% probability that the sum of the digits is odd.
c. 0.24 = 24% probability that the number is greater than 70.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We are given the prime numbers less than 100, they are:
2,3,5,7,11,13,17,19,23,29,31,37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
There are 25 prime numbers less than 100.
a. The number is odd
Of the 25, 24 are odd, only the number 2 is even. So
24/25 = 0.96 = 96%
0.96 = 96% probability that the number is odd.
b. The sum of the digits is odd
The sum of the digits is odd for:
3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89. So for 12 of them
12/25 = 0.48 = 48%
0.48 = 48% probability that the sum of the digits is odd.
c. The number is greater than 70
71, 73, 79, 83, 89, 97. 6 of them
6/25 = 0.24 = 24%
0.24 = 24% probability that the number is greater than 70.
A) The probability that one of the numbers is odd is; 96%
B) The probability that the sum of the digits is odd is; 48%
C) The probability that the number is greater than 70 is; 25%
We are given the prime numbers;
2,3,5,7,11,13,17,19,23,29,31,37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
This is a total of 25 prime numbers.
Thus; N = 25
A) The number of odd numbers are 24.
Thus,probability of selecting an odd number is;
P(odd number) = 24/25
P(odd number) = 0.96 or 96%
B) The numbers that their sum is odd are:
3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89
Kindly note that the single numbers are added to zero to make them odd too.
Thus there are 12 of them that their sum are odd.
P(sum is odd) = 12/25
P(sum is odd) = 0.48 or 48%
C) The numbers that are greater than 70 from the list are 71, 73, 79, 83, 89, 97. This is a total of 6 numbers.
Thus;
P(number is greater than 70) = 6/25
P(number is greater than 70) = 0.25 or 25%
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n is an odd number.
Which statements are true?
You must get them all correct to get any marks.
A: n²-1 is odd
E: n(n-2) is odd F: (n-2)² is odd
B: n(n-1) is odd C: (n-1)² is odd
D: n² + 2 is odci
Answers
Answer:
True:
D.
E.
F
Step-by-step explanation:
First, you should know that the square of any odd number is also odd.
The easiest way to go about this is to plug in an odd number for n. Lets use 3:
Plug 3 into A:
\(3^{2} -1=9-1=8\)
Plug 3 into B:
\(3(3-1)=9-3 = 6\)
Plug 3 into C:
\((3-2)^{2} = 2^{2} = 4\)
Plug 3 into D:
\(3^{2} +2 = 9+2=11\)
Plug 3 into E:
\(3(3-2) = 9-6 = 3\)
Plug 3 into F:
\((3-2)^{2}=1^{2} =1\)
In ΔQRS, q = 6.8 inches, r = 1.9 inches and ∠S = 141° . Find the length of s, to the nearest 10th of an inch
Answers
c = 141 s =
150 inch
help please. really need answers to understand
Answers
Answer:
hmmmm.... each question here is relatively straight forward, the issue is that these questions basically represent an entire unit (possible two) of an Algebra II class... I can provide answers, but the explanation (if you don't know the basic ideas might be elusive, But I will try to help)
Step-by-step explanation:
1) A = P (1+ r/n) ^ nt
interest equation ... monthly compounding so n = 12 thus r gets divided by 12 and t get multiplied by 12
A = 10,000(1 + .04/12)^(3*12)
A = 10000(1.00333)^36
A = $11,272.71
========================
2) \(A = pe^{rt}\)
A = 15,000 \(e^{.06 t}\)
18,000= 15,000 \(e^{.06 t}\)
1.2= \(e^{.6 t}\)
ln(1.2) = .06t (ln e)
.1823 / .06 = 3.03 years
Note: ln e = 1
==========================
\(3^{5x+1} = 27\)
\(3^{5x+1} = 3^{3}\)
thus: 5x+ 1 = 3
5x = 2
x = 2/5
==============================
f(x) = 5x - 12
y = 5x - 12
inverse
x = 5y - 12
5y = x + 12
y = 1/5 x + 12/5
=====================
fog(X) =
f(X) =6x+12
g(x) = x^2 + 3
fog(X) = 6(x^2 + 3)+12
= 6x^2 + 18 + 12
= 8x^2 + 30
Domain (- infinity, + infinity)
======================
vertex 3x^2 - 6x + 2
verted = [-b/2a, f(-b/2a)]
a=3 , b=-6 , c = 2
-b/2a = 6/6 = 1
f(-b/2a) = -1
vertex = (1,-1)
=======================
30x - .4x^2
-30/-.8 = 37.5
max rev = 30(37.5) - .4(37.5)^2 = $562.5
The corporate team-building event will cost $56 if it has 7 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $80? Solve using unit rates.
Answers
Answer:
10
Step-by-step explanation:
56 ÷ 7 = 8 each.
80 ÷ 8 = 10
PLZ HELP MEEE ASAP PLZZZZZ
