To find the value of Mary's investment after 2 years in a saving account with compound interest, we can use the compound interest formula. Substituting the given values into the formula gives us £12363.61.
Explanation:To calculate the value of Mary's investment after 2 years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:
A is the final amountP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times the interest is compounded per yeart is the number of yearsIn this case, the principal amount is £12000, the annual interest rate is 1.5% (0.015 as a decimal), and the number of times the interest is compounded per year is 1. Plugging these values into the formula, we get:
A = 12000(1 + 0.015/1)^(1*2)
Simplifying this, we get:
A = 12000(1.015)^2
Calculating further, we get:
A ≈ 12000(1.030225) ≈ £12363.61
Therefore, the value of Mary's investment after 2 years is approximately £12363.61.
Solve the quadratic equation of 2x^2-5x+1=0
"suppose we are comparing the implementations of algorithm a and algorithm b on the same machine. for inputs of size n, algorithm a runs in 2n steps, and algorithm b runs in 5√n steps. for which values of n does algorithm a beat algorithm b?"
The solution is : n = 9
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Explanation:
To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:
1000*n*n = n*n*n*n*n
1000 = n*n*n = n^3
n = ∛(1000) = 10 (when n equals ten A equal B)
For any integer greater than ten B > A and for any integer smaller than ten B < A.
The greatest integer for which B < A is nine, therefore nine is our answer.
A B
1000n^2 n^5
n = 8 64000 < 32768
n = 9 81000 < 59049
n = 10 100000 = 100000
n = 11 121000 > 161051
n = 12 144000 > 248832
therefore nine is our answer.
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For [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex], Algorithm A (which runs in [tex]\( 2n \)[/tex] steps) beats Algorithm B (which runs in [tex]\( 5\sqrt{n} \)[/tex] steps).
To determine for which values of [tex]\( n \)[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:
Algorithm A runs in [tex]\( 2n \)[/tex] steps.
Algorithm B runs in [tex]\( 5\sqrt{n} \)[/tex] steps.
Algorithm A beats Algorithm B if [tex]\( 2n < 5\sqrt{n} \)[/tex].
Let's solve this inequality step by step:
1. Square both sides to eliminate the square root (valid since [tex]\( n \geq 0 \)[/tex]):
[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]
[tex]\[ 4n^2 < 25n \][/tex]
2. Bring all terms to one side to form a quadratic inequality:
[tex]\[ 4n^2 - 25n < 0 \][/tex]
3. Factorize the quadratic inequality if possible:
[tex]\[ n(4n - 25) < 0 \][/tex]
4. Find the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\( n(4n - 25) < 0 \)[/tex] holds when one factor is negative, and the other is positive:
[tex]\( n < 0 \)[/tex] and [tex]\( 4n - 25 > 0 \)[/tex]: No valid solutions since [tex]\( n \geq 0 \)[/tex].
[tex]\( n > 0 \)[/tex] and [tex]\( 4n - 25 < 0 \)[/tex]:
[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]
[tex]\( n < 0 \) and \( 4n - 25 < 0 \)[/tex]: All [tex]\( n \geq 0 \)[/tex] satisfy this condition.
5. Determine the integer values of [tex]\( n \)[/tex]:
Since [tex]\( n \)[/tex] must be non-negative, the integer values of [tex]\( n \)[/tex] that satisfy [tex]\( 4n^2 - 25n < 0 \)[/tex] are [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex].
the letters that spell WAIKIKI are each written on separate tiles laying face down on a table. A tile is selected at random, the letter is recorded, and then the letter is placed face down on the table. Then the process repeats. What is the theoretical probability of choosing a tile with the letter A?
A. 1/7
B. 1/4
C. 2/7
D. 3/7
Answer:
the Answer is. A 1/7
Step-by-step explanation:
i did the test
Find the radius of convergence of the power series \sum_{n=1}^\infty \frac{x^n}{\root 9 \of n}
Write 7.085 × 10-14 as an ordinary number
To convert [tex]7.085 * 10^-{14}[/tex] to an ordinary number, move the decimal point 14 places to the left, resulting in 0.00000000000007085.
Explanation:To write [tex]7.085 * 10^-{14}[/tex] as an ordinary number, you need to move the decimal point 14 places to the left because the exponent is negative. This means the number is very small. The process is similar to changing other numbers from scientific to standard notation, for example, changing [tex]7.5 x 10^{-3}[/tex] to 0.0075 by moving the decimal point three places to the left.
For [tex]7.085 * 10^-{14}[/tex], you will end up with 0.00000000000007085. The number has thirteen zeros after the decimal point and before the 7085 because we move the decimal 14 places.
Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8
how do you solve 3 - 1 3/4
Latrell bought 4 bags of powdered sugar. He got a total of 5 1/2 cups of sugar. How many cups of sugar were in each bag?
Each bag contained 1.375 cups of sugar.
To find out how many cups of sugar were in each bag that Latrell bought, we need to divide the total amount of sugar by the number of bags. Latrell has a total of 5 1/2 cups of sugar, which is the same as 5.5 cups when converted to a decimal. He bought 4 bags of sugar. Therefore, the calculation we need to perform is:
5.5 cups / 4 bags = 1.375 cups per bag
So, each bag contained 1.375 cups of sugar.
Use the distributive property to write the products as sums:7(4n-5m-2)
The distributive property is used to multiply 7 by each term inside the parentheses (4n, -5m, -2) resulting in the expression 28n - 35m - 14.
Explanation:To apply the distributive property to the expression 7(4n-5m-2), you multiply each term inside the parentheses by 7. The distributive property allows us to multiply a single term outside a parenthesis with each term inside the parenthesis, effectively distributing the multiplication.
First term: 7 × 4n = 28nSecond term: 7 × -5m = -35mThird term: 7 × -2 = -14Therefore, the product written as a sum, using the distributive property, is 28n - 35m - 14.
10 POINTS!!! I WILL GIVE BRAINLIEST!
Bens barbeque charges a setup fee to $52 for catering a barbeque party plus an additional $6.25 per person. Robert is planning to hire Ben's barbeque to cater a picnic. Robert has no more than $175 to spend on the picnic. What is the greatest number of people who can attend the picnic? (*WRITE AND SOLVE AN INEQUALITY TO SOLVE THIS PROBLEM*)
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→8 x2 − 64 x2 − 8x
Take the limit as x approaches 8 to get the answer of 9.
Explanation:To find the limit of (x² - 64) / (x² - 8x) as x approaches 8, we can simplify the expression by factoring and cancelling common factors.
First, we factor in the numerator and denominator:
x² - 64 = (x + 8)(x - 8) and x² - 8x = x(x - 8).
Now we can cancel the common factor of x - 8 to simplify the expression: (x + 8)/(x).
Now, we can take the limit as x approaches 8:
Lim(x→8) (x + 8)/(x) = 8 + 8/8
= 9.
So the limit of the given expression as x approaches 8 is 9.
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Find tanθ exactly if sinθ=-9/41, and θ is in the fourth quadrant
how many tiles in figure 0? Where is the Y intercept?
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds, find the frequency when the tension is 72 pounds.
Answer:
when the tension is 72 pounds , the frequency is 900 hertz
Step-by-step explanation:
Hello, I think I can help you with this.
you can easily solve this by using a rule of three.
According to the question data:
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:
f ∝ √T
where f is the pitch or frequency and T is the tension
Step 1
if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds
300 hertz ∝ √8 pounds
300⇔√8
what is the frequency when the tension is 72 pounds
x⇔√72
Step 2
Let
300⇔√8
x⇔√72
the relation is
[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]
when the tension is 72 pounds , the frequency is 900 hertz
have a good day.
The Junior Soccer League takes 12-person vans to the tournament. The league has 146 players and 14 coaches. How many vans are needed and how many people are left over?
Final answer:
The Junior Soccer League will need a total of 14 vans to transport 160 people, with 4 people left over after filling the 13th van.
Explanation:
To calculate the number of 12-person vans needed for the Junior Soccer League event, we first need to determine the total number of people that require transportation. This includes both players and coaches.
We have 146 players and 14 coaches, giving us a total of 160 people. If each van holds 12 people, the next step is to divide the total number of people by the capacity of the van.
Divide the total number of people by the capacity of the van (12).Calculate the number of full vans required.Determine if there are any people left over.160 ÷ 12 = 13 vans with 4 people left over because 12 vans can only carry 144 people (12 × 12), and 16 people are remaining, which requires another van to accommodate them.
So, the league will need a total of 14 vans for transportation, and there will be 4 people left over after filling the 13th van.
If a drug has a concentration of 350 mg per 10 mL, how many milliliters are needed to deliver 2 grams of the drug? Express your answer rounded to the nearest milliliter.
To deliver 2 grams of a drug with a concentration of 350 mg per 10 mL, convert 2 grams to milligrams (2000 mg), and then divide this value by the concentration in mg/mL (350 mg/10 mL) to find the volume in milliliters. After calculation, this results in approximately 6 milliliters, when rounded to the nearest milliliter.
Explanation:To calculate how many milliliters are needed to deliver 2 grams of the drug when the concentration is 350 mg per 10 mL, we start with the conversion of grams to milligrams since the concentration is provided in milligrams. Remember, 1 gram equals 1000 milligrams:
Convert 2 grams to milligrams: 2 grams × 1000 = 2000 mg.Determine how many milliliters provide 350 mg: 10 mL corresponds to 350 mg.Calculate the proportion: (2000 mg) / (350 mg/mL) = Number of milliliters needed.Perform the calculation: 2000 / 350 = 5.71428571 mL.Round to the nearest milliliter: Approximately 6 mL.Therefore, approximately 6 milliliters of the drug are needed to deliver a dose of 2 grams.
the following shows a sequence of perfect cube
64,p,216,q
find the value of p+q
Saylor Henshaw earned $120 in simple interest in 9 months at an annual interest rate of 5%. How much money did he invest?
Saylor Henshaw invested $1600.
Explanation:To find out how much money Saylor Henshaw invested, we can use the formula for simple interest:
Interest = Principal × Rate × Time
In this case, Saylor earned $120 in 9 months at an annual interest rate of 5%.
Let's assume the principal amount is P.
Using the formula:
120 = P × 0.05 × (9/12)
Simplifying the equation, we have:
P = 120 ÷ 0.05 × 12/9
P = $1600
So, Saylor Henshaw invested $1600.
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Use this equation to find dy/dx. 9y cos(x) = x2 + y2
Final answer:
The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).
Explanation:
The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).
Let's differentiate both sides:
The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)
The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)
Equating both the derivatives, we have:
9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)
Now, solving for dy/dx gives us:
dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)
choose the equation below that represent the line that passes through the point (7,-2) and has a slope of -3
The first truck in a convoy will carry 12 tons of dirt while each additional truck will carry 8 tons of dirt. Write a rule to model th situation. Then use the rule to find how many tons of dirt can be carried by 7 trucks. Let n represent the number of trucks and t represent the tons of dirt.
Final answer:
To model the situation, use the rule t = 12 + 8(n - 1), where n is the number of trucks. Applying this rule, 7 trucks can carry a total of 60 tons of dirt.
Explanation:
The student should write a rule to model the situation where the first truck carries 12 tons of dirt and each subsequent truck carries 8 tons. The rule can be defined as t = 12 + 8(n - 1), where n represents the number of trucks and t represents the total tons of dirt carried. For 7 trucks, we can plug in the value of n into the equation:
t = 12 + 8(7 - 1)
t = 12 + 8(6)
t = 12 + 48
t = 60 tons
Therefore, 7 trucks can carry a total of 60 tons of dirt.
Find a formula for the function whose graph is given below.
The equation of parabola is y = ( x - 2 )² + 3
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The vertex of the parabola is given as A ( 2 , 3 )
Now ,
The equation of parabola is given by
y = a ( x - h )² + k
where the vertex of the parabola is A ( h , k )
a = 1
So , substituting the values of vertex in the equation of parabola , we get
y = ( x - 2 )² + 3
Hence , the equation of parabola is y = ( x - 2 )² + 3
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10 mi.= _________ft.
_____ require a date signature amount and pay to the order of. (1 point)
Credit Cards
Debit Cards
Checks
Loan Documents
The answer is; c.) checks!
what is the interqueartile range for the data set 13,14,17,18,23,27,28,31,34
The price of a technology stock has risen to $9.73 today. Yesterday's price was $9.60 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
There are 25 students performing in their holiday concert. Of students 11 are boys. What decimal represents the fraction of the students that are boys
Jimmy has a number cube labeled 1through 6, and a penny. How many different ways can the cube and penny land with one roll of the cube and one flip of the penny . 1. 2. 3. 4. 5. 6
Answer:
12 ways
Step-by-step explanation:
We know that,
When the cube is rolled,
Possible ways = 6 ( i.e. 1, 2, 3, 4, 5 or 6 ),
While, when a penny is flipped,
Possible ways = 2 ( i.e. head or tail ),
Thus, when the cube and penny flipped one time,
Total possible ways = 6 × 2 = 12
( i.e, 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T or 6T )
Melody jackson wishes to enclose a rectangular garden with fencing, using the side of her garage as one side of the rectangle. a neighbor gave her 30 feet of fencing, and melody wants the length of the garden along the garage to be 3 feet more than the width. what is the length of the garden? write your answer without units.
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Solve the Equation
-2=3x/5+1