The interest that Harry will earn altogether if he puts £23000 in the account for 5 years is £386,538,000.
Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. For an amount, compound interest is computed using both the principal and accrued interest. This is the primary difference between compound and simple interest.
Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
In mathematics, compound interest is frequently referred to as C.I.
It is possible to compute interest using both the initial principle and interest that has accumulated over time.
Compound interest is calculated mathematically as Amount - Principal, where
Amount = Principal*(1 + (r/n))t, where r is the rate of interest, n is the number of times interest is compounded annually, and t is the number of years, and Principal is the initial amount deposited.
Given, Principal = £23000
Rate of interest = 6%
Number of times interest is compounded per year = 1
Number of years = 5
Using above literature, Amount = 23000(1 + (6/1))^5 = 23000*16807 = £ 386,561,000.
Thus, Compound Interest = £386,561,000 - £23000 = £386,538,000.
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For scenarios of statistical studies are given below. Decide which study is a sample statistic
EXPLANATION
Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).
Beginning with 23 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given byy = 23(1/2)^t/45, t ≥ 0.How much of the initial mass remains after 170 years? (Round your answer to three decimal places.)
1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:
[tex]\begin{gathered} y=23(\frac{1}{2})^{\frac{t}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}}^ \\ y\approx1.677 \end{gathered}[/tex]2) So, according to this model we can tell there will be left approximately
[tex]1.677g[/tex]Give a counterexample to the following conditional statement. Write your answer as a number. If |x+ 4|= 8, then x=−12
he Solution:
iven in the question that if
[tex]|x+4|=8\text{ then x=-12}[/tex]We are required to give a counterexample to the given conditional statement above.
[tex]\begin{gathered} |x+4|=8 \\ \text{Means that} \\ x+4=8\text{ or x+4=-8} \end{gathered}[/tex]Solving each of the equations above, we get
[tex]\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \\ Or \\ x+4=8 \\ x=8-4 \\ x=4 \\ \text{ So, } \\ x=-12\text{ or x=4} \end{gathered}[/tex]So, the counterexample to the given conditional statement is x = 4.
Question four need to know what I did wrong I need to do it I need to understand
If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.
As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.
So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.
-7×+8=-4x = ? trying to understand this
Here, we want to get the value of x
We can get this by isolating x
We start by bringing like terms together
[tex]\begin{gathered} -7x\text{ = -4-8} \\ \\ -7x\text{ = -12} \\ \\ x\text{ = }\frac{-12}{-7} \\ \\ x\text{ = }\frac{12}{7} \end{gathered}[/tex]What is the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births? (Equal chance of any)
the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.
What is the difference between permutation and combination in probability?For a list of data, where the order of the data is important, a permutation is used, while for a group of data, where the order of the data is irrelevant, a combination is used.Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!the possible outcomes are
BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG
wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.
We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities
P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)
=[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]
= 3/8.
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The number must be a one digit number, When the number is added to 746 the digit in the ones place of the sum is less than the ones digit in 746.
The one digit numbers that when added to 746 gives a digit in the ones place of the sum which is less than the ones digit in 746 are;
4, 5, 6, 7, 8, or 9
What is a place value?Place values is the value a digit in a number posseses based on its position in the number
The given parameters of the number are;
The number of digits in the number = 1
The ones digit of the sum of the number and 746 is less than the ones digit in 746, which is 6
Therefore;
The value of the number when added to 746 can be expressed as 7xy
Where;
y < 6
The process of adding two numbers involves the addition of the numbers based on their place values such that the ones digit part of the result is placed as the output while the 1 in a result that is 10 or more is added to the next higher place value number to the left of the added digits
Therefore, to have a value of the digit in the ones place less than 6, we can have;
746 + 0 = 746
746 + 1 = 747
746 + 2 = 748
746 + 3 = 749
746 + 4 = 750; 0 < 6746 + 5 = 751; 1 < 6746 + 6 = 752; 2 < 6746 + 7 = 753; 3 < 6746 + 8 = 754; 4 < 6746 + 9 = 755; 5 < 6The possible one digit numbers that gives a sum with a ones digit less than 6 when added to 746 therefore includes; 4, 5, 6, 7, 8, and 9
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How many solutions does the equation. a| x + b | + c = d have when a > 0 and c = d? When a < 0 and c > d ? Explain your reasoning.
In the first case the equation has only one unique solution and in the second case the equation has many solutions.
We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as
a|x + b| + c = d
a|x + b| = d - c, since c = d then we can write equation as
a|x + b| = 0, Now, a > 0
=> |x + b| = 0
=> x = -b that is only one unique solution.
Now, in second case a < 0 and c > d then
a|x + b| = d - c
If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.
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Find the slope of the line graphed below.
Answer:
[tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
There are two blue dots on the graph. It does not matter which dot you startr at. Let's start at the bottom, right dot. How many space up and to the left you do you have to move to get to the second dot?
You need to move 5 dots straight up. Up is a positive direction. Then you have to move 2 spaces left. Left is a negative direction, so your slope will be negative.
- [tex]\frac{5}{2}[/tex] [tex]\frac{-5}{2}[/tex] [tex]\frac{5}{-2}[/tex] All of these mean the same thing.
Pls help and thanks!
the multiplication of 2 matrices A and B
a11 a12 a13 ...
a21 a22 a23 ...
a31 a32 a33 ...
...
b11 b12 b13 ...
b21 b22 b23 ...
b31 b32 b33 ...
is
a11×b11+a12×b21+a13×b31+... a11×b12+a12×b22+a13×b32 ...
a21×b11+a22×b21+a23×b31+... a21×b12+a22×b22+a23×b32
a31×b11+a32×b21+a33×b31+... a31×b12+a32×b22+a33×b32
...
in other words, we combine the rows of the first matrix with the columns of the second matrix.
the rows of the result matrix are driven by the rows of the first matrix and the columns of the second matrix.
formally :
we can multiply a m×n matrix only with a n×o matrix.
the number of columns in the first matrix must be equal to the number of rows in the second matrix.
the result matrix is then sized m×o.
the first element (first row first column) of the result matrix is the sum of the products of the elements of the first row of the first matrix with the elements of the first column of the second matrix.
the element in the (x,y) position in the result matrix is the sum of the products of the elements of the xth row of the first matrix with the elements of the yth column of the second matrix.
so, when multiplying 2 2×2 matrices, the condition is automatically fulfilled : m = n = o = 2
ST =
4×0+1×-4 4×4+1×3
-3×0+-2×-4 -3×4+-2×3
=
-4 19
8 -18
and TS =
0×4+4×-3 0×1+4×-2
-4×4+3×-3 -4×1+3×-2
=
-12 -8
-25 -10
as we can see, the 2 results are completely different.
Perform the following division: -48 / 5
A. 9.6
B. 8.1
C. -8.1
D. -9.6
If f (x) = -3x - 2, find the value
ƒ(-7)
Answer:
19
Step-by-step explanation:
-3(-7)-2
21-2
19
it need to be at least 20 chqracters so ignore this the answer is at the top
Find the common difference and the next two terms of the arithmetic sequence.11,19,27,35The common difference isWrite the next two terms in the sequence:11,19,27,35,?,?
The common difference in the given arithmetic sequence is 8.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.So, formula for common differences:
d = (aₙ₊₁ - aₙ)Now, insert terms in the formula as follows:
d = (aₙ₊₁ - aₙ)d = (19 - 11)d = 8Therefore, the common difference in the given arithmetic sequence is 8.
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 22 feet more than the length of the shortest side. Find the dimensions if the perimeter is 186 feet.
The three sides of the triangle will be 82, 63, and 41 feet.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.
That a flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side 22 feet more than the length of the shortest side.
Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.
Perimeter = A + B + C
A = 2B and C = 22 + B
Put the values in the equation as solve:-
Perimeter = A + B + C
186 = 2B + B + 22 + B
186 = 4B + 22
4B = 186 - 22
4B = 164
B = 164 / 4
B = 41 feet
Longest side = 2B = 2 x 41 = 82 feet
Shirtest side = B = 41 feet
Third side = 22 + B = 22 + 41 = 63 feet
Therefore, the three sides of the triangle will be 82, 63, and 41 feet.
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When x =1/2 and y = 1/8, -5x + 14y =
Answer:
-5x1/2= -2.5 14x1/8= 1.75
Step-by-step explanation:
-2.5+1.75=-0.75
Answer:
-3/4
Step-by-step explanation:
Plug in values of x and y into expression:
[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]
[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]
Find common denominator:
[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]
[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]
Solve numerator:
[tex]14-20=-6[/tex]
So,
[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]
Solve each system by graphing, and then write the solution. x + 4 = - y-6y + 9x = - 6
To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.
According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).
how do i do vertical analysis
To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.
What is a vertical analysis?Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.
The base figure is the revenue in the income statement or the total assets in the balance sheet.
The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.
Examples of vertical analysis can be shown with AT$T and Verizon below:
AT&T Percent
Revenue $132,447 100%
Cost of Services (Expenses) 60,611 45.8% ($60,611/$132,447 x 100)
Selling & Marketing Expense 39,697 30.0%
Depreciation & other expenses 20,393 15.4%
Operating Income $11,746 8.9%
Verizon Percent
Revenue $127,079 100%
Cost of Services (Expenses) 49,931 39.3% ($49,931/$127,079 x 100)
Selling & Marketing Expense 41,016 32.3%
Depreciation & other expenses 16,523 13.0%
Operating Income $19,599 15.4%
Thus, we have performed the vertical analysis of AT$T and Verizon above.
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Question Completion:Income Statements of AT&T and Verizon (in millions) are:
AT&T Verizon
Revenue $132,447 $127,079
Cost of Services (Expenses) 60,611 49,931
Selling & Marketing Expense 39,697 41,016
Depreciation & other expenses 20,393 16,523
Operating Income $11,746 $19,599
A dealer sold a watch 130% of his cost. If the sale price was $39, how much did the cost the dealer? Please show your work.
The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.
As given in the question,
Sale price of the watch for which dealer sold = $39
Let $'x' be the cost of the watch with which dealer purchase
A dealer sold a watch 130% of its cost
Required expression to show the given condition of a dealer is given by:
130% of x = $39
⇒ (130 /100) × x = $39
⇒ x = ( 39 × 100 ) / 130
⇒ x = $30
Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.
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The Faulk Corp. has a bond with a coupon rate of 4 percent outstanding. The Gonas Company has a bond with a coupon rate of 10 percent outstanding. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
If the interest rates suddenly rise by 2 percent, the percentage change in the price of these bonds are : 19.73%, 16.56%.
Percentage changeUsing this formula to find the current price of a bond
P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n
Where:
P =Current price of a bond
C = Coupon payment,
YTM = Yield to maturity
n = Time to maturity
F =Face value of a bond
The Faulk Corp. bond
C = Coupon rate / number of payments per year × face value = 4% / 2×$1,000 = $20
n = 13 years = 36 half-year periods
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
hence,
P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $405.81 + $289.83
P=$695.61
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.
Price of the Faulk Corp. bond:
P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $353.32 +$205.03
P=$558.38
Percentage change:
Percentage change = $558.38 - $695.61/$695.61×100%
Percentage change =19.73%
Gonas Company bond:
C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50
n = 18 years = 36 half-year periods,
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $1,014.52 + $289.83
P=$1,304.35
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :
P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $883.30 +$205.03
P=$1,088.33
Percentage change:
Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%
Percentage change =16.56%
Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.
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4 ≤-3x - 1≤9
What is the compound inequality
Answer:
−1≤x<3
Step-by-step explanation:
−4≤3x−1<8
−4≤3x−1and3x−1<8
3x−1≥−4and3x−1+1<8+1
3x≥−3and3x<9
x≥−1andx<3
−1≤x<3
The bill for dinner was $61.66. You left $10.34 for the tip. What percentage of the original bill was the tip? Round your a
to the nearest whole percent.
Answer:
17%
Step-by-step explanation:
You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.
PercentageA percentage is a fraction that has been multiplied by 100%:
10.34/61.66 × 100%
≈ 0.168 × 100%
≈ 17%
The tip was about 17% of the original bill.
Part 1 of 2
Your friend says that the solutions to the inequality 6x-19x≤52 are xs-4. Solve the inequality correctly. What error did your friend
make?
3 is grater than or equal to W and -5 is less than W write as an inequality
Answer: 3 ≥ W > -5
Step-by-step explanation:
Just look at the way the question is asked, that is the best I can explain. Sorry.
Classify each as corresponding, AIA, AEA, CIA,
or CEA
1)
3)
5)
X
y
2)
4)
++
When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1. A small ice cream freezer requires 10 cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?
Answer:
When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1.
Select all the equations where x = 3 is a solution.X-3 = 01 + x = 209 - x= 3O 6 = 2xOf = 3x2 = 9
Let's begin by listing out the given information:
[tex]undefined[/tex]Element X is a radioactive isotope such that every 20 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 770 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answer:
[tex]t = 18.9[/tex]
Information given :
We know that:
- Element X is a radioactive isotope such that every 20 years, its mass decreases by half
- the initial mass of a sample of Element X is 770 grams
And we must find how long it would be until the mass of the sample reached 400 grams
Step-by-step explanation:
To find it, we need to use the following formula:-
[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]
- A(0) is the initial amount
From given information, A(0) = 770 grams
Now, replacing the value in t :
[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]
Then, we must solve for t :-
[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]
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a fellow comrade,
Cheers !
What is the maturity value given the following:$10,800 at 8% for 8 months
The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as
I = PRT
where
I is the interest after time t
P is the principal or initial amount
R is the interest rate
T is the time in years
From the information given,
P = 10800
R = 8/100 = 0.08
T = 8 months
We would convert 8 months to years. Recall,
12 months = 1 yr
8 months = 8/12 = 0.67
Thus,
t = 0.67 yr
By substituting these values into the formula, we have
I = 10800 x 0.08 x 0.67
I = 578.88
Thus,
Maturity value = 10800 + 578.88
Maturity value = $11378.88
Determine which of the following proportions are true.I 1mi2hr=12mi24hrII 7min9cents=36min24centsIII
1 and 3
1 * 12 = 12
2 * 12 = 24
so 1 is true
7 * 5.14 = 36
9 * 5.14 = 46.26
so 2 is not true
7 * 4 = 28
2 * 4 = 8
so 3 is true
Name:
Math for College Liberal Arts
Classifying Data and Frequency Tables
Classify the following variables as qualitative (C) or quantitative (Q). (1 point each)
1. A list of telephone numbers:
3. Types of animals at a zoo :
11th graders
12th graders
Students at a local high school in grades 11 and 12 are asked what gaming system they
prefer. The results are summarized below in a two-way frequency table.
5. Complete the table. (6 points)
TOTAL
Nintendo Switch
132
11th graders
12th graders
TOTAL
Date:
?
?
2. Heights of players on a basketball team
4. Number of children in a family:
PS4
?
127
?
Neither
?
PS4
95
182
TOTAL
?
Use the table above to answer these questions. (1 point each)
6. How many 12th graders do not like either gaming system?
7. How many total students like the Nintendo Switch?
8. What is the total number of 11th grade students?
9. How many total students are there?
10. How many 11th graders like the PS4?_
11. Create a relative frequency table from the table above. Write the relative frequencies as decimals
rounded to two decimal places. (12 points)
Nintendo Switch
Neither
315
655
TOTAL
Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."
What are qualitative variables and quantitative variables?Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.
Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.
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