The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
Given that the interest is compounded continuously.
For the given situation the formula of compound interest is:
[tex]A = Pe^{rt}[/tex]
where, A is the amount = $12300
P is the principal amount
r is the rate = 4% = 0.04
t is the time = 8 years
Substituting the values we have:
[tex]12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461[/tex]
Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
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You teach an arts and crafts class at your local library. There are 12 girls and 11 boys registered for the class. You
need to purchase supplies that will cost $5 per student.
How much will it cost to purchase the supplies?
$28
$67
$71
$115
$192
Answer:
$115
Step-by-step explanation:
12 + 11 = 23
There are 23 students in the class.
Cost of supplies: $5 per student.
total cost = 23 × $5 = $115
The total cost to purchase the supplies is,
⇒ $115
What is mean by Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
There are 12 girls and 11 boys registered for the class.
And, You need to purchase supplies that will cost $5 per student.
Here, Total students = 12 + 11 = 23
Hence, The total cost to purchase the supplies is,
⇒ 23 x $5
⇒ $115
Thus, The total cost to purchase the supplies is,
⇒ $115
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15.
Mrs Dixon puts 230 eggs into boxes.
Each box holds 12 eggs.
How many egg boxes does Mrs Dixon need to put all the eggs into boxes?
Answer:
20 boxes
Step-by-step explanation:
Each box ca hold 12 eggs
There are 230 eggs
So you will need 230/12 = 19 1/6 boxes = 19.167 boxes
Since you cannot get less than 1 box, round up to 20 boxes. There will be some empty spaces in one of the boxes
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 180 liters of 22% acid solution?
Answer:
22% = 163.63636364 litres.
50% = 409.090909 litres
Step-by-step explanation:
when 22% acid solutions = 180 litres
then 20% acid solutions = ?
therefore =
[tex] = \frac{20}{22} \times 180 \\ = \frac{3600}{22} \\ = 163.63636364.litres[/tex]
Also when 22% acid solutions = 180 litres
then 50% acid solutions = ?
therefore
[tex] = \frac{50}{22} \times 180 \\ = \frac{9000}{22} \\ = 409.090909.litres[/tex]
therefore 22% = 163.63636364 litres.
50% = 409.090909 litres.
Consider the function R(t) as representing the value of an ounce of palladium in U. S. Dollars as a function of the time t in days. †
R(t) = 210 + 30t^3; t = 1
Find the average rate of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0. 1, and 0. 01 days. (Use smaller values of h to check your estimates. ) (Round your answers to one decimal place. )
h = 1, h = 0. 1, h = 0. 01
what are the Average Rate of change? (for each h)Estimate the instantaneous rate of change of R at time t, specifying the units of measurement. R'(1) = ___ dollars/day
The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.
The average rate of change of a function is the ratio of how much the output of the function changes over a given period to the length of that period. We can calculate this for the function R(t) = 210 + 30t3 by considering the time intervals [t, t+h] at h = 1, 0.1 and 0.01 days.
For h = 1 day, the average rate of change of R(t) is 90 dollars/day. This can be calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+1)3 = 1080, by the length of the period, h = 1 day.
For h = 0.1 day, the average rate of change of R(t) is 900 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.1)3 = 9, by the length of the period, h = 0.1 day.
For h = 0.01 day, the average rate of change of R(t) is 9000 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.01)3 = 0.9, by the length of the period, h = 0.01 day.
The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.
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Help!! Math is really hard!!! Can someone explain how they got this?
Yes!
[tex](2^{2} )^{3}[/tex] = 2^6 = 64
(8-4)^2 = 4^2 = 16
then for the last part
4^-4 is the same as [tex]1/4^{4}[/tex] or 1/256
Then it is order of operations:
do 16 x 1/256 first which is 1/16
and then 64 - 1/16 to get 63 15/16 :)
Determine the solution to the system of equations represented by the tables below.
-3 -2
-1 0
6
4
2 0
X
f(x)
X
g(x)
-2
7
-1
2
0 1
-3-8
Answer:
(-1, 2)
Step-by-step explanation:
The solution to a system of equation will always intersect on a graph, which means that at a certain point, they will have the same x and y coordinate.
As we can see from the table, for both f(x) and g(x) when x = -1, y = 2, which is the intersection point.
What are the coordinates of the center in the measure of the radius for a circle whose equation is (x-10)^2+(y-3)^2=36
Answer:
Center is (10, 3)
Radius = 6
Step-by-step explanation:
The standard equation of a circle is
(x - a)² + (y - b)² = r²
where
(a, b) is the center of the circle and
r is the radius
Comparing (x - 10)² + (y - 3)² = 36
it is easy to see that a = 10, b = 3 and r =√36 = 6
So center is(10, 3) and radius is 6
question 10
help me asap
Note that the lenght of segment LN = 55.14 (Option D)
This is arrived at using the Chord Bisector Theorem and the lengths of the sides of a right-angled triangle.
What is the Chord Bisector Theorem?According to the theorem, the line that goes through the circle's center and is perpendicular to the chord also bisects it.
This means that LK (as per the attached image) is the same as MK.
The Right Angle Postulate also means that:
LX = √[KX² - LK²]
LX = √[29² - 9²]
LX = √(841 81)
LX = √760
LX = 27.57
Since LN = LX *2
LN = 27.57 * 2
LN = 55.14
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4) Write 5√5 + √20 in the form a√5
5) Write √5 x √8 in the form b√10
6) Write √600-√24 in the form a√6
Answer:
4) 7 SqrRt( 5 )
5) 2 SqrRt( 10 )
6) 8 SqrRt( 6 )
Jonathan rides his bicycle at a velocity of 12 m/s East. He
comes to a hill and over the next 23 seconds, his velocity
decreases to 5 m/s East. What is Jonathan's acceleration?
Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Jonathan's initial velocity, u = 12 m/s East
His final velocity, v = 5 m/s East
The time taken, t = 23 seconds
We can use the formula for acceleration:
a = (v - u) / t
Substituting the given values, we get:
a = (5 m/s - 12 m/s) / 23 s
a = -7 m/s / 23 s
a = -0.3043 m/s^2 East
Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
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AQRS is an isosceles triangle. Complete the statement that explains whether RT is the height of the triangle.
√85 cm.
Q
R
11 cm
T 6 cm S
Since 62+(√85)
height of AQRS.
112, RT
is
is not
the
In the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
Given ,
AQRS is an isosceles triangle. Complete the statement that explains whether RT is the height of the triangle.
So, from the given triangle we can say that ,
[tex]6^{2}[/tex] + [tex]\sqrt{85 }^2[/tex] = [tex]11^{2}[/tex]
By the pythagorean theorem , we can say that ,
the sum of squares of base and opposite side is always equals to square of hypothenuse.
so it is equal to square of 11 and RT is height.
Therefore, in the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.
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On a hot summer day, Brad and his friends decided to have a water fight. They threw water balloons for 33 minutes. When all the water balloons were gone, they sprayed water with hoses for 32 minutes. The water fight ended at 4:28 P.M. when Brad's dad showed up with ice cream. What time did the water fight start?
Answer:
3:23
Step-by-step explanation:
The water fight ended at 4:28 and lasted for 32 minutes so
4:28 - 32 minutes = 3:56
3:56 - 33 minutes = 3:23
14. Refer to the figure. Prove that AC is perpendicular to BC.
Answer:
∴Sum of interior angles in ΔABC = 180°
∠A + ∠B + ∠C = 180°
2x° + 4x° + 6x° = 180°
12x° = 180°
= x =
∴x = 15
∴∠C = (6)×(15)
= 90°
This means AC makes a 90° angle (i.e. ∠C) with BC.
∴AC is perpendicular to BC (Proved)
Also ΔABC is a right-angled triangle
Please help find the missing side length using trig!
The missing side length is x = 30
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side
from the given figure,
tan 37° = x/40
0.75 = x/40
x = 30
Therefore, The missing side is 30.
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Can Someone tell me the answer for this one pleas:
Determine which integers in the set S:{−4, 4, 6, 21} make the inequality 3(j − 5) > 3(7 − 2j) true.
S:{6, 21}
S:{4, 21}
S:{−4, 6}
S:{−4, 4}
The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.
An inequality response is defined?
An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.
The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.
First, we will simplify the given inequality.
3(j-5)>3(7-2j)
⇒j-5>7-2j
⇒3j>12
⇒j>4
It means that numbers greater than 4 will satisfy the given inequality.
Numbers greater than 4 in the given set are 6,21.
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What is the solution set to the inequality w+ 4<4 (w - 2)?
Select a ray. Move the point on the ray to the correct place on the number line.
-7 -6 -5 -4
H
->
(-)
-3 -2 -1
0 1 2
--
31
3
4 5 6 7
--
+
The solution set to the inequality is w > 3
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
w+ 4<4 (w - 2)
Open the bracket
So, we have the following representation
w+ 4 < 4w - 8
Evaluate the like terms
So, we have the following representation
12 < 3w
Divide by 3
4 < w
So, we have
w > 4
See attachment for number line
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How many solutions does the system have?
O One solution at (0,-4)
O One solution at (-3,0)
O No solution
O Infinitely many solutions
The system of equations has infinite solutions.
How to solve thisGiven:
y = -6x +2
-12x - 2y= -4
To solve for Equation 2,
The value of y is already given in equation 1,
Thus,
substituting the value of y in equation 2,
-12x -2(-6x +2) = -4
-12x - 12x = -4 +4
0=0
The solution of the two equations is 0. Also, we can see that both equations are in ratio.
Further, the image also shows that the line of the two equations are coinciding.
Hence, the system of equations has infinite solutions.
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How many solutions does this linear system have?
y = -6x +2
-12x - 2y= -4
one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.
Divide 12x5 - 36x4 - 6x³ by 6x².
O 2x² + 6x + 1
O 2x² - 6x - 1
2x³ + 6x² + x
O 2x³-6x²-x
Answer:
D. 2x^3−6x^2−x
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
Hope this helps.
Reeta has spent 2/7 of her salary on car repair work. She has 15. 000 rupees left with her. What is her salary?
As per unitary method, Reeta's salary is 21,000 rupees.
The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.
In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.
Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:
2/7 * x
Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:
2/7 * x = x - 15,000
Simplifying this equation, we get:
2x = 7(x - 15,000)
2x = 7x - 105,000
5x = 105,000
x = 21,000
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Find the surface area of a cylinder with radius 5.9 ft and height 4.4 ft. Use a calculator. Round to the nearest tenth.
The surface area of a cylinder with radius 5.9 ft and height 4.4 ft is 381.8 square feet.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the the surface area of a cylinder with radius 5.9 ft and height 4.4 ft.
The surface area of cylinder=2πr(r+h)
r=5.9
h=4.4
The value of pi is 3.14
The surface area of cylinder=2×3.14×5.9(5.9+4.4)
=37.052(10.3)
=381.8 square feet.
Hence, the surface area of a cylinder with radius 5.9 ft and height 4.4 ft is 381.8 square feet.
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sara is making punch. she has 15 cups of sugar. each batch of punch needs 1.25 cups of sugar. how many batches of punch can sara make?
Answer: 12
she has 15 cups of sugar and needs 1.25 cup for a batch so we say 15/1.25 to get 12
Answer:
12
Step-by-step explanation:
15 / 1.25 = 12 she can make 12 batches
Gina wilson all things algebra unit 4: congruent triangles homework 7: proofs review: all methods page 1
In geometry, two triangles are said to be congruent if they are the same size and shape. This means that all corresponding angles and sides are equal.
To prove that two triangles are congruent, we must use one of the five congruency tests: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).The SSS test states that if all three sides of two triangles are equal, then the triangles are congruent. The SAS test states that if two sides and the included angle of two triangles are equal, then the triangles are congruent. The ASA test states that if two angles and the included side of two triangles are equal, then the triangles are congruent. The AAS test states that if two angles and a non-included side of two triangles are equal, then the triangles are congruent. Lastly, the HL test states that if the hypotenuse and a leg of a right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.In order to prove that two triangles are congruent, we must show that one of the five congruency tests is true. To do this, we can use techniques such as the Reflexive Property, the Symmetric Property, and the Transitive Property. We can also use logical reasoning, such as if two angles are equal and their corresponding sides are proportional, then the triangles must be congruent.
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What is the definition of congruent triangles?
5x-2=2x+15
5x-2x=15+2
3x=17
Answer:
[tex]x = \frac{17}{3} = 5\frac23 = 5.\overline6[/tex].
Step-by-step explanation:
No idea what your question is, but [tex]x = \frac{17}{3} = {5\frac23} = 5.\overline{6}[/tex].
Question 3 of 10
The function a(b) relates the area of a trapezoid with a given height of 14 and
one base length of 5 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
a(b)=14. D+5
2
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. b(a)=+7
B. b(a)--7
O C. b(a)- +5
OD. b(a)-2-5
Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.
What is the area of a Trapezoid?Recall that the function for the trapezoid area is:
A(x)=(B+b)*h/2
where
B and b are the bases and
h is the height.
Thus, given a height of 14 and one base length of 5 with the length of its other base
With the given data: h=14 B and b =5 and x (it may vary which one is bigger)
So that function becomes:
A(x)=(5+x) * 14/2
A(x)=(5+x)*7
So if you want the inverse function, you have to operate to find x:
A(x)/7=5+x
A(x)/7-5=x
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Does the set of odd integers have the density property? Explain.
It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true
How to explain the informationThe set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.
Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.
Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.
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Two sides of a triangle are
shown. Find the range of
values of the third side.
10, 5
< X
Answer:
5 < x < 15
Step-by-step explanation:
The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side
In the given triangle we are provided measures of two of the sides as 10 and 5
Let the measure of the third side be x
So the three sides are 10, 5 and x
Then by the inequality theorem
10 + 5 > x
==> 15 > x or
x < 15 This is an upper bound for x
when we switch sides in an inequality > changes to < and < changes to >
We also have
x + 5 > 10 ==> x > 10 - 5 ==> x > 5
and
x + 10 > 5 ==> x > -5
Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x
Combining all inequalities we get
5 < x < 15
Note
We could also state the lower and upper bound limits as
difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5
or
5 < x < 15
While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students
x/2+4x=2 pls send a good explanation
Dr. Grumman got his first job in 2020. In that year, the government took out 6.2% of a person's
income for Social Security, until a person made $137,700. If Dr. Grumman earned $141,340 in
2020, how much did he pay to Social Security?
The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
What are percentages?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages: (Value/Total value) * 100
Dr. Grumman earned $141,340 in 2020.
The social security he paid is:
(141340)(6.2/100) = 8763.08
Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
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18y-5= -17x in slope intercept form
Answer:
y = -17/18x + 5/18
Step-by-step explanation:
isolate the y so add five to the other side
18y = 5 + -17x
divide everything by 18
18y/18 -17x/18 5/18
y= -17/18x + 5/18
A teacher gave a 25 question multiple choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this information........ (choose the correct choice) None of the above. she must have made a mistake. about half the scores were above the mean. all the students had the same score.
By applying standard deviation concept, it can be concluded that all the students had the same score.
The mean is the average of all the scores. It is calculated by adding up all the scores and dividing them by the number of scores.
The standard deviation is a measure of how spread out the scores are. It is calculated by finding the difference between each score and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.
If all the scores are the same, then the difference between each score and the mean will be 0. This means that the standard deviation will also be 0. Therefore, the correct answer is "all the students had the same score."
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