Answer:
Step-by-step explanation:
20
please help asap. due monday
if I am correct that is the solution.
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
The value of her investment at compound interest after 4 years will be £8934.34.
What is compound interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.
Given,
Principal (P) = £8000
Rate of interest (r) = 2.8% compound interest p.a.
Time (n) = 4 years
Then, according to compound interest compounded annually,
Amount = P(1+r/100)ⁿ
= 8000(1+2.8/100)⁴
= 8000(102.8/100)⁴
= 8934.34
Hence, the value of her investment at compound interest after 4 years will be £8934.34.
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the
unit cost is given by the function C(x)=0.5x²-180x+25,885. What is the minimum unit cost?
Do not round your answer.
Answe(0.5x²-180x+25,885= 47,925.25
Step-by-step explanation:
x=1
7, 5, 2, 1
For the sequence above:
i.) Find the general term
ii.) Find the next three terms
iii.) Hence- find the 25th term
The sequence 7, 5, 2, 1, then the
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
The sequence is,
⇒ 7, 5, 2, 1
[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]
( i ) . The general term,
Let us assume general term = d
We can use this formula,
d = [tex]a_{n+1} -a_{n}[/tex]
where,
[tex]a_{n+1} = 5\\a_{n} = 7[/tex]
d = 7 - 5
d = 2
So,
The general term d = 2
( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]
We can use this formula,
[tex]a_{n+1} =a_{n} +d[/tex]
[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]
[tex]a_{5} = 1+2\\a_{5} = 3[/tex]
[tex]a_{6} = 3+2\\a_{6} = 5[/tex]
[tex]a_{7} = 5+2\\a_{7} = 7[/tex]
So,
The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term
We can find nth term,
We can use this formula,
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n} = 7+(n-1)2[/tex]
[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]
Then, 25th term is,
We can substitute n = 25
[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]
So,
The 25th term [tex]a_{25}[/tex] = 55
Therefore,
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
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Zander downloads a combination of 30
games and songs. He downloads 8
more songs than games. The equation g+(8+g)=30
can be solved to determine g
, the number of games Zander downloaded. How many games and songs did Zander download?
Zander Downloaded _ games and _ songs
Would someone help me please and thank you
Zander downloaded a total of 19 Songs and 8 Games.
In the given question, it is stated that Zander's downloads had a combination of 30 games and songs in which he downloaded 8 songs more than games. The equation representing the given situation is g + (8 + g) = 30. Here, g represents Games, and (g+8) represents songs.
Now, to find out the number of games and songs, we need to calculate the value of g by the equation.
=> g + (8 + g) = 30
=> 2g + 8 = 30
=> 2g = 22
=> g = 11
We get value of g = 11, So, downloaded games will be 11 and songs will be 19
Hence, the number of Games and Songs will be 11 and 19 respectively.
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You have a $25 calling card. Calls made using the card within the United States cost $.10 per minute while calls made from the US to France cost $.25 per minute. a. Write an inequality that relates the number of minutes ‘x’ you can use for calls within the U.S. and the number of minutes ‘y’ you can use for calls from the U.S. to France.
The inequality that represents the number of minutes of calls made in the United States and in France, can be presented as follows:
The inequality that represents the duration of calls that can be made in the United States: 0 ≤ x ≤ 250The inequality that represents the number of minutes of calls that can be made in France using the calling card is: 0 ≤ y ≤ 100What is an inequality in mathematics?An inequality expresses the relationship between two or more values that are not equal.
The value of the calling card = $25
The cost of calls made in the United States = $0.10
Cost of calls made in France = $0.25
The number of minutes that can be used for calls in the U.S. = x
The number of minutes that can be used for making calls in France = y
The duration of calls that can be made in the United states is therefore:
[tex]x_{max} = \dfrac{\$25}{\$0.10} = 250[/tex]
The inequality that represents the number of calls that can be made in the United States is therefore: 0 ≤ x ≤ 250
The duration of calls that can be made in France with the $25 calling card is therefore: [tex]y_{max}=\dfrac{\$25}{\$0.25} = 100[/tex]
The inequality that represents the number of minutes the calling card can be used in making calls in France is: 0 ≤ y ≤ 100
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Line E passes through the points (-3, 4) and (2, 7). What is the slope of a line perpendicular to line E?
The slope of a line perpendicular to line E is -(5/3).
How do you calculate slope of a perpendicular line?By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m₂ = -1/m₁ if the slope of the provided line is m₁ and the slope of a perpendicular line is m₂.Given:
Line E passes through the points (-3, 4) and (2, 7).
Slope of line E = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{7-4}{2-(-3)}[/tex]
= [tex]\frac{3}{5}[/tex]
So, the slope of a line perpendicular to line E will be the negative reciprocal of the slope of line E i.e. -(5/3).
Therefore, the slope of a line perpendicular to line E is -(5/3).
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Solve the inequality 1/4 (x-20)<-6 or -6x+5≤-1. Write your solution in algebraic form, interval notation, and graphed on a number line.
The solution of the given inequality is:
x ≥ 1.
And the graph on the number line can be seen in the image at the end.
How to solve and graph the inequality?
The inequality we want to solve and graph is:
-6x + 5 ≤-1
To solve this, we need to start by isolating the variable x in one of the sides, we will get:
-6x + 5 ≤-1
-6x ≤-1 - 5
-6x ≤ -6
Now we can divide both sides by -6 to get:
x ≥ 1.
Then the graph will be like the one below. You need to have a closed dot on x = 1 (because that is a solution to the inequality) and then shade all the region to the right of x = 1, because x also can be larger than 1.
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80p as a fraction of £3
simplest form
Answer:
Step-by-step explanation:
4/15
Based on the concept of fraction, 80p is equivalent to 4p/15p as a fraction of £3.
What is a fraction?Fraction is a term that is used to describe the portion or part of the whole thing.
Generally, the term fraction represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator.
In this case, to find the fraction of 80p as a fraction of £3, we divide 80p by £3.
Since there are 100 pence in 1 pound the fraction can be expressed as 80p/£3.
To simplify the fraction divide both the numerator and the denominator by 10:
80p/£3 = 8p/30p
Simplifying further both the numerator and the denominator can be divided by 2:
8p/30p = 4p/15p
Therefore, in this case, it is concluded that 80p is equivalent to 4p/15p as a fraction of £3.
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the sum of 2 numbers is 96. the larger number is 9 less than 4 times the smaller. find boh nmbers.
The sum of 2 numbers is 96, this can be expressed as
[tex]x+y=96[/tex]The larger number is 9 less than 4 times the smaller, this can be expressed as
[tex]x=4y-9[/tex]Now, we replace the second equation in the first one
[tex]\begin{gathered} 4y-9+y=96 \\ 5y=96+9 \\ y=\frac{105}{5} \\ y=21 \end{gathered}[/tex]We use this number to find x.
[tex]x=4\cdot21-9=84-9=75[/tex]Hence, the numbers are 75 and 21.Look at this angle:
What is the vertex?
Answer:
T. The vertex is where the angle is measured. It is often associated as the vertex angle.
Step-by-step explanation:
Hope it helps! =D
Answer:
T is the vertex
Step-by-step explanation:
the point where the angle lies , is the vertex, in this case T
using the letters forming the angle , with the vertex T placed in the middle
∠ STU or ∠ UTS
Divide. Express your answer in scientific notation.
7.2x 10-4
3x10-3
7.2x10-4
3x10^-3
(Use scientific notation. Use the multiplication symbol in the math palette as needed.
The value of 7.2 × 10^-4 divided by 3 × 10^-3 when expressed in scientific notation is 2.4 × 10^-7.
What is scientific notation?It should be noted that scientific notation is simply used to illustrate the numbers that are either too large or too small. It is denoted as a × 10ⁿ.
It should be noted that the exponents will be added. Therefore, 7.2 × 10^-4 divided by 3 × 10^-3 will be:
= 7.2 × 10^-4 / 3 × 10^-3
= 2.4 × 10^-7.
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Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
The pencils and erasers that each student have is 14.
How to calculate the value?From the information, the person has 56 pencils and 42 erasers and wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers.
It should be noted that this has to do with looking for the highest common factor.
The highest common factor for 56 and 42 is 14.
The students will have 14 pencils each.
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ing Equations Practice
CONCEPT: Multi-Step Equations
C Level:
What is the value of x? Show your work and explain how you found the answer.
-4x-43 = -95
Answer:
X:15
Step-by-step explanation:
only a genius can explain i can ask my colic to help
six tickets to a movie cost 76.50 what constant of proportional relates the number of tickets and total cost
Based on the number of movies, $12.75 is the constant of proportionality per movie
How to determine the constant of proportionality?The given parameters are
Number of the movie tickets = 6
Cost of the movie tickets = 76.50
The constant of proportionality of the movie tickets is calculated as
Constant of proportionality = Cost of the movie tickets/Number of the movie tickets
Substitute the known values in the above equation
So, we have
Constant of proportionality = 76.50/6
Evaluate the quotient
So, we have
Constant of proportionality = 12.75
Hence, the constant of proportionality per movie is $12.75
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Answer:
Step-by-step explanation:
$12.75
The formula for the volume of a cylinder with a base radius equal to 3 inches (in) is shown below. v ≈28.3h where v=volume and h=height What is the closest estimate of the height of the cylinder if the volume is 200 in ³?
Answer:
7 inches
Step-by-step explanation:
π * 3^2 *7 = 197.920337
A plumber have an estimate for the renovation of a kitchen. Her hourly pay is $26 per hour and the plumbing parts will cost $80 flat. If her total estimate is $366, how many hours does she expect this job to take?
I need to show work too so please help!! thank you!
Answer:
11 hours
Step-by-step explanation:
let x represent the hours worked
26(x) + 80 = 366
26(x)=366-80
26(x)=286
x=11
.˙. the plumber worked 11 hours
The length of Rectangle A is 5 inches more than its width. The perimeter of Rectangle B is 17. The difference between the perimeters of the rectangles is less than 9. What are the possible integer values for the width of Rectangle A? 1in. 2in. 3in. 4in.5in. 6in. 7in. 8in.
Answer:
Step-by-step explanation:
Let L and W be the length and width of a triangle.
Rectangle perimeter (Px) = 2L + 2W, where x is triangle a or b.
Rectangle A: La = 5Wa [The length of Rectangle A is 5 inches more than its width.]
Perimeter Rectangle A: Pa = 2La + 2Wa
Substitute L = 5Wa:
Pa = 2La + 2Wa
Pa = 5Wa + 2Wa
Pa = 7Wa
Perimeter Rectangle B: Pb = 17 [The perimeter of Rectangle B is 17]
Pb = 17
Difference between Pa and Pb: Is it < 9?
See the attached table. The perimeters of rectangle A are computed for each of the answer options that define the width. Length (rectangle A) is 5 inches more than the width. The perimeter is 2*Length + 2*Width, and shown as Pa.
The perimeter of rectangle b is 17, shown as Pb on the table. The last column of the table is the absolute value of the difference of Pa and Pb. If it is less than 9, the cell is green (it is a possible integer value for the width of rectangle A), Red mean it does not meet the "less than 9" requirement, One cell has the difference as 9. The problem states "less than 9," so it does not meet the requirement.
two packages of strawberries are sold for $10. how much could you buy with $25?
F.) 3
G.) 4
H.) 5
J.) 6
K.) 7
Answer:
G.) 4
Step-by-step explanation:
If you get two packs of strawberries for $10, with another $10 you could get another two packs. 2+2=4, and 10+10=20. So you could get 4 packs with with $20.
can u please help me on b guys ty
Answer:
circle is 22
Triangle is 34
Step-by-step explanation:
22 + 22 + 22 = 66
22 + 34 + 34 = 90
Take 90 - 22 = 68
Divide 68 by 2 to get 34
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Less than or equal to (≤).Less than (<).Greater than or equal to (≥).Greater than (>).In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:
Let w represent the number of weeks.
Translating the word problem into an algebraic equation, we have;
Volunteering hours = 52 hours.Remainder of her volunteer hours = 3w hours.Total time to graduate (at least) = 90 volunteer hours.Next, we would combine the above parameters to form an algebraic equation as follows:
52 + 3w ≥ 90
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Complete Question:
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
answer choices
A. 52w + 30w ≥ 90
B. 52w + 30w ≤ 90
C. 52 + 3w ≤ 90
D. 52 + 3w ≥ 90
Jenna is making knit hats for Christmas presents.
Each hat requires her to use 1 1/3 yards of yarn. If she has 30 yards of yarn, how many hats can she make?
This problem is asking me to determine?
Write the equation you will be using to solve.
Answer:
22 hats
Step-by-step explanation:
30÷1 1/3=22.5
The question is implying how many completed hats she can make, and since half a hat is not completed, she can only make 22 completed hats.
Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 13 and hypotenuse labeled 16
square root of 425
square root of 3
square root of 29
square root of 87
hypotenuse = 16
perpendicular = 13
base= ?
By using pythogoras theroem :
H² = P² + B²
16² = 13² + B²
256 = 169 + B²
B² = 256 -169
=87
B² = 87
B = √87
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Answer: The correct answer is D - square root of 87
Step-by-step explanation: I took the test and I got it right.
Have a good day/night :)
Solve the answer
100*0.5=a
a*2=
Answer:
a = 50
50*2=100
Step-by-step explanation:
if y=3x write 5y in terms of x
explanation?
The value of 5y in terms of x in the equation is 5y = 15x
How to solve equation?The equation is given as y = 3x
Therefore, we are ask to find 5y in terms of x.
This simply means we have to make 5y the subject of the formula in the equation.
In other words, we have to isolate 5y in terms of x in the equation.
Therefore,
y = 3x
multiply both sides by 5
5 × y = 3x × 5
5y = 15x
Therefore,
5y = 15x
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Mr. Lou teaches 7 reading groups. Each reading group has 5 students. Find how many total
students Mr. Lou teaches today if 3 students are absent.
Which expression correctly represents the problem?
7x (5-3)
(7x5)-3
KC
7-(5 x 3)
D
(7-5) x 3
11
Based on the number of reading groups, and the number of absent students, the expression for the problem is (7 x 5) - 3.
How to find the expression?Every reading group taught by Mr. Lou has 5 students. There are also 7 reading groups. This means that the total number of students under Mr. Lou is:
= Number of reading groups x Number of students per group
= 7 x 5
Then out of this total number, 3 students are absent. The expression then becomes:
= Number of students - Number o absent students
= (7 x 5) - 3
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-2
Step-by-step explanation:
-2y^2=-2y^2
What is rate of change for 3=2x-21
Answer:
Step-by-step explanation:
I believe I need 2 variables to properly work this out but x=12
3=2x-21
24=2x
12=x
you know x is a number less than 4. Select all the inequalities that must be true
The inequality is (3,∞) < x < 4.
What is an inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given Data
x is a number less than 4
x<4
Numbers which are less than 4 are 3 to infinity
So,
The inequality is:
(3,∞) < x < 4
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Answer the questions about the following function.
f(x) =
X+11
X-9
(a) Is the point (3,-9) on the graph of f?
Answer:
No
Step-by-step explanation:
I just graphed f(x)=x+11, f(x)=x-9, and (3,-9) in Desmos, and you can visibly see that it isn't.