Answer:
qr rs st qt are the line hope it helped
21. A rectangle has an area of 24 square inches. Let W be the
width (in inches), L be the length (in inches), and A be the
area (in square inches).
a. Sketch three possible rectangles of area 24 square inches.
b. Which of the symbols W. L. and A are variables? Explain.
Which of the symbols W, L. and A are constants? Explain.
Three possible rectangles of area 24 square inches are:
A rectangle with width 6 inches and length 4 inches
A rectangle with width 8 inches and length 3 inches
A rectangle with width 4 inches and length 6 inches
How to explain the areaIt should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.
In this case, W and L are variables and A is a constant.
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Suppose that the world's current oil reserves is R = 2090 billion barrels. If, on average, the total reserves is decreasing by 18 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R , in terms of t , the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R = B.) 15 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)
a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.
b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.
c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.
What is a linear equation?A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.
A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.
The current total world oil reserves, R = 2,090 billion barrels
Average decrease per year = 18 billion barrels
a) Linear equation for R is 2,090 - 18t
b) In 15 years, the total oil reserves = 2,090 - 18(15)
= 2,090 - 270
= 1,820
c) The constant rate of decrease = 18 billion barrels per year
The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).
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Find the sample variance and standard deviation.
23, 16, 5, 7, 11 q
OA. s² =
2
S
OB. 0²=
The sample variance and the standard deviation are 52.8 and 7.26
How to determine the sample variance and standard deviationFrom the question, we have the following parameters that can be used in our computation:
23, 16, 5, 7, 11
Calculate the mean
Mean = (23 + 16 + 5 + 7 + 11)/5
Mean = 12.4
The standard deviation is
SD = √[Sum of (1 - Mean)²]/[N - 1]
So, we have
SD = √[(23 - 12.4)² + (16 - 12.4)² + (5 - 12.4)² + (7 - 12.4)² + (11 - 12.4)²]/[5 - 1]
This gives
SD = √211.2/4
So, we have
SD = √52.8
SD = 7.26
Hence, the standard deviation is 7.26
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Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4).
The volume of the parallelopiped is 4
How to solve for the volumeWe have to solve this with the use of matrix system in math
PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)
we have to find
Q - P
(-1, 6, 5) - (-3, 3, 2)
= (2, 3, 3)
R - P
R(-4, 2, 1) - (-3, 3, 2)
= ( -1 , -1, -1)
S - P
S(3, 1, 4) - (-3, 3, 2)
= (6 , -2, 2)
we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]
the determinant of the matrix is the volume
2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]
= -8 - 12 + 24
= 4
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"The scores X on a pretest for a college statistics course and the course grade Y were recorded for 10 students. The results are as follows: X ---- 75,81, 57, 79, 68, 93, 96, 84, 41, 89 Y ----- 2, 3, 1, 2, 1, 4, 4, 3, 1, 3 What might you conclude?"
A. There is absolutely no correlation between the scores and grades
given.
B. There is a very weak correlation between the scores and grades given.
C. There is a moderate correlation between the scores and grades.
D. There is a strong correlation between the scores and grades.
Answer:
Step-by-step explanation:
C. There is a moderate correlation between the scores and grades.
Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.
The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.
In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.
However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.
In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $19. Construct a confidence interval at a 80% confidence level.
Give your answers to one decimal place.
Answer:
{40.7,49.3}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{80\%}=45\pm1.282\biggr(\frac{19}{\sqrt{32}}\biggr)\\ \\CI_{80\%}\approx45\pm 4.3\\\\CI_{80\%}=\{40.7,49.3\}[/tex]
Thus, we are 80% confident that the true sample mean amount spent is between $40.70 and $49.30
Please help me with this question :(
1. The amount of pizzas which the pizzeria must sell for employees to receive the bonus is 78.
2. The new number of pizzas sold is considered as percent increase of 20%.
How many pizzas must the pizzeria sell for employees to receive the bonus?The pizzeria sold 65 pizzas yesterday and the owner offers bonus if the number sold increases by 20% today. The number that must be sold, to receive a bonus is computed as follows:
= 65 pizza * (65 pizza * 20%)
= 65 pizza * 13 pizza
= 78 pizza.
Is the number of pizzas sold as a percent increase or decrease?It is a percent increase which is computed as follows. The formula for percentage increase is: ((Final value - Initial value)/Initial value * 100).
The Percent increase:
= (78 pizza - 65 pizza) / 65 pizza.
= 13 pizza / 65 pizza
= 0.2
= 20%
Full question "A local pizzeria sold 65 pizzas yesterday. (step 1) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. (Part 2) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work. Answer:"
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What song form is the song. "Shameless" by Billy Joel written in?
A. Verse-chorus-bridge
B. AABA
C. ABACA
D. Verse-chorus
Help with questions pls?
does the equation y^2-y^2x = 6 describe y as a function of x
The equation y² - y²x = 6 can be describe as a function of x as:
y = √(6/(x - x)).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y² - y²x = 6
Taking y² as common.
y²(1 - x) = 6
Divide both sides with (1 - x).
y² = 6/(1 - x)
Square root on both sides.
y = √(6/(x - x))
This is a function of x.
Thus,
y = √(6/(x - x)) is a function of x.
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A school is having a movie day. They are selling popcorn at the school for $0.50 per bag. If a student purchases popcorn with $5, how much popcorn would the student receive?
This student would receive 10 bag of popcorns.
How to determine the quantity of popcorn?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;
Number of bag of popcorns = Cost of one bag of popcorn/Unit price
Substituting the given parameters into the mathematical expression above, we have the following;
Number of bag of popcorns = 5/0.50
Number of bag of popcorns = 10 bag of popcorns.
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In a class of 30 students x +10 study algebra, 10+3 study statistics, 4 study both algebra and statistics. 2x study only Algebra and 3 study neither algebra nor statistics
1. Illustrate the information one a Venn diagram.
2. How many students study;
A. Algebra
B. Only statistics
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
a. Algebra = 128/11b. Statistic = 213/11When the statistics students number = 2·x + 3, we have;
The number of students that study
a. Algebra = 16b. Statistic = 15How to solve thisThe parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10Number of students that study statistics n(B) = 10·x + 3Number of student that study both algebra and statistics n(A∩B) = 4Number of student that study only algebra n(A\B) = 2·xNumber of students that study neither algebra or statistics n(A∪B)' = 3Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 2711·x+13 = 27 + 4 = 31=11·x = 18x = 18/11The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
The Venn diagrams can be presented as follows;
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For the following distribution of quiz scores, how many individuals took the quiz?
x f
5 6
4 5
3 5
2 3
1 2
a. 5
b. 10
c. 15
d. 21
The answer is not one of the given choices. The correct answer is 73.
To find the total number of individuals who took the quiz, we need to add up the frequency (f) for each score (x) and then take the sum:
5(6) + 4(5) + 3(5) + 2(3) + 1(2) = 30 + 20 + 15 + 6 + 2 = 73
Therefore, the answer is not one of the given choices. The correct answer is 73.
Frequency distributions are portrayed as frequency tables or charts. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In the latter instance, the distribution is called a relative frequency distribution.
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You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much money would you save by shopping in the physical store after all discounts, taxes, and shipping fees have been applied?
Item Quantity Physical Store Online Store
Batteries 2 packs $5.99/pack $4.99/pack
Stereo 1 system $100.00/system $90.00/system
CDs 3 CDs $7.95/CD $8.95/CD
A)It is more expensive to shop in the physical store.
B0$19.62
C)$9.94
D)$0.46
The solution is Option D.
The difference in shopping from store and online is given by the equation D = $ 0.46
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of shopping in physical store be A
Let the total cost of shopping online be B
Now , the equations will be
The number of batteries = 2
The number of stereo = 1
The number of CDs = 3
The cost of buying 2 packs of batteries from store = 2 x ( 5.99 ) = $ 11.98
The cost of buying 1 stereo from store = 1 x ( 100 ) = $ 100.00
The cost of buying 3 CDs from store = 3 x ( 7.95 ) = $ 23.85
The total purchase cost without discount and sales tax = $ 135.83
The cost with 10 % discount = $ 122.247
The cost after 5 % sales tax = $ 128.35935
So , the total cost of shopping in store A = $ 128.35935
And ,
The cost of buying 2 packs of batteries online = 2 x ( 4.99 ) = $ 9.98
The cost of buying 1 stereo from online = 1 x ( 90 ) = $ 90.00
The cost of buying 3 CDs from online = 3 x ( 8.95 ) = $ 26.85
The total purchase cost without discount and sales tax = $ 126.83
The cost with $ 5 discount = $ 121.83
The shipping cost in online store = $ 121.83 + $ 6.99 =
So , the total cost of shopping in online store A = $ 128.82
Now , the difference in shopping from store and online is
D = $ 128.82 - $ 128.35935
On simplifying the equation , we get
D = $ 0.46
Hence , the equation is D = $ 0.46
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Find the value of x.
The angles x and 3x - 12 are two vertical angles and the measure of the vertical angle x is equal to 48°.
What are vertically opposite anglesVertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.
We shall evaluate for the measure of x as follows:
x + x + 3x - 12 + 3x - 12 = 360° {sum of angles at a point}
2x + 6x - 24 = 360°
8x - 24 = 360°
8x = 360° + 24 {add 24 to both sides}
8x = 384°
x = 384°/8 {divide through by 8}
x = 48°
Therefore, since the angles x and 3x - 12 are two vertical angles we have derived the measure of the vertical angle x to be equal to 48°.
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Answer:
x = 42°
Step-by-step explanation:
Please here it is.
Augustus is generally selfish and somewhat unpopular at school. He decides that
he could improve his image by sharing his candy with everyone at school. When he
has a pile of 100,000 candies, he generously plans to give away 60% of the candies
that are in the pile each day. Although Augustus may be earning more candies for
doing his homework, he is only giving away candies from the pile that started
100,000 (He's not that generous!)
Graph
The number of pieces of candy that will be left on day 4 would be 2, 560 candies .
The number of pieces of candy left on day 8 would be 66 candies .
How to find the number or candy left ?To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:
= Number of starting candy x ( 1 - Percent given away ) ^ number of days
= 100, 000 x ( 1 - 60 % ) ⁴
= 100, 000 x 40 % ⁴
= 2, 560 candies
On Day 8, this would be:
= 100, 000 x ( 1 - 60 % ) ⁸
= 66 candies
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The question is:
How many pieces of candy will be left on day 4? On day 8?
please help me with math i’ll give you brainlist
The linear functions for this problem are classified as follows:
a. Parallel.
b. Neither parallel nor perpendicular.
c. Perpendicular.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.They are classified as parallel, perpendicular or neither according to their slopes as follows:
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A suspect has two months of unpaid fees. One month they had 3 parking tickets and 14 traffic violations totaling $2030.The second month they had 11 parking tickets and 11 traffic violations totaling $2200 . How much does each parking ticket cost? How much does each traffic violation cost?
Answer:
each parking ticket costs $100 and each traffic violation costs $124.28.
Step-by-step explanation:
To find out the cost of each parking ticket and each traffic violation, we can set up two equations using the information given:
Let x be the cost of each parking ticket.
In the first month, 3 parking tickets cost 3x, and 14 traffic violations cost 14y.
The total cost for the first month is 2030, so we have:
3x + 14y = 2030
In the second month, 11 parking tickets cost 11x, and 11 traffic violations cost 11y.
The total cost for the second month is 2200, so we have:
11x + 11y = 2200
Now that we have two equations, we can use substitution to find the value of x and y.
From the first equation, we can solve for y:
y = (2030 - 3x) / 14
Substituting this expression for y into the second equation:
11x + 11((2030 - 3x) / 14) = 2200
Expanding the expression for y and simplifying the equation:
11x + 2030 - 33x / 14 = 2200
Multiplying both sides by 14:
154x + 28420 = 30800
Solving for x:
x = $100
So each parking ticket costs $100, and each traffic violation costs:
y = (2030 - 3x) / 14 = (2030 - 3 * 100) / 14 = (2030 - 300) / 14 = 1730 / 14 = $124.28
Therefore, each parking ticket costs $100 and each traffic violation costs $124.28.
Answer:
-727.41 dollars
Step-by-step explanation:
To find the cost of each parking ticket and each traffic violation, we can set up a system of two equations. Let's call the cost of a parking ticket "x" and the cost of a traffic violation "y".
For the first month:
3x + 14y = 2030
For the second month:
11x + 11y = 2200
We can solve for x and y using any method, such as substitution or elimination. For this problem, let's use substitution.
First, we'll solve for x in the first equation:
3x + 14y = 2030
3x = 2030 - 14y
x = (2030 - 14y) / 3
Next, we'll substitute this expression for x into the second equation:
11x + 11y = 2200
11((2030 - 14y) / 3) + 11y = 2200
2030 - 14y + 11y = 2200 * 3 / 11
2030 - 3y = 636
-3y = -1394
y = 464.67
Finally, we'll substitute this value of y back into the first equation to find x:
3x + 14y = 2030
3x + 14(464.67) = 2030
3x = 2030 - 6544.68
x = (2030 - 6544.68) / 3
x = -2180.23 / 3
x = -727.41
So each parking ticket costs approximately -727.41 dollars, and each traffic violation costs approximately 464.67 dollars. However, since these values are negative, it means the suspect has received a credit rather than being charged for these fees.
Help me with this question…..
Answer:
A.
Step-by-step explanation:
Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])
Suppose you have a deck that is 16ft. By 24ft. An 8ft by 4in board costs $7.50. How much will the material costs?
Answer:
45
Step-by-step explanation:
Please helpppppp!!!!
Answer:
x(f)- this is the correct answer
a.find the profit function
B.find the marginal profit function
C.find marginal average profit function
D. use marginal analysis to estimate the profit from the sale of 201st doll
a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 12x + 300√x - 2500.
b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x) is dP/dx = 12 + 300/2√x.
c. The marginal average profit function is the derivative of the profit function divided by the number of units sold is dP/dx ÷ x = (12 + 300/2√x) ÷ x.
d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201 is $16.62.
What do you mean by profit function?
A profit function is a mathematical model that represents the profit made from selling a certain product or service as a function of the number of units sold. The profit function is calculated as the difference between the total revenue and the total cost of producing and selling the product.
Mathematically, if R(x) represents the total revenue from selling x units of a product and C(x) represents the total cost of producing and selling x units of the product, then the profit function can be represented as P(x) = R(x) - C(x).
a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have:
P(x) = 14x - (2x - 300√x + 2500)
P(x) = 12x + 300√x - 2500
b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x):
dP/dx = 12 + 300/2√x
c. The marginal average profit function is the derivative of the profit function divided by the number of units sold.
dP/dx ÷ x = (12 + 300/2√x) ÷ x
d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201:
P(201) = 12 * 201 + 300 * √201 - 2500 = $3347.09
Since we want the profit from the sale of one unit, we divide the profit by 201:
P(201) ÷ 201 = $16.62
So, the estimated profit from the sale of the 201st doll is $16.62.
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emma has 0.5 lb of sugar. How much water would she add to make the following concenstractions? Tell Emma how much syrup she would have each case. 50% syrup
To make the concentration of 50% syrup,
she needs to add 0.5 lb of sugar.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."
Given:
Emma has half a pound of sugar.
To make the concentration of 50% syrup:
Let n be the required amount.
In decimals, 50% is 0.5.
Applying the percentage formula;
we get,
[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]
Applying cross multiplication,
we get,
[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]
0.5 = 0.5(n + 0.5)
1 = n + 0.5
n = 1 - 0.5
n = 0.5 lb.
Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.
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Find the equation for the line through the points (2,3) and (7,1)
Answer:
Step-by-step explanation:
m=3-1/2-7= -2/5
c⇒ -2
y=mx+c
y=-2/5x-2
Wilson Montgomery was curious about the difference between a simple discount note and a simple interest note. He is considering taking out one or the other. Let him know which one he should take out based on proceeds and effective rate. Both have the same terms: $5,500 at 6% for 18 months. Round to the nearest tenth.
What is the answer to this question?
Based on the proceeds and effective rate, Wilson should take out the simple discount note, which has a higher proceeds of $5,005 and a higher effective rate of 9.9% compared to the simple interest note's proceeds of $5,995 and effective rate of 9.0%.
How to take out based on proceeds and effective rate?To compare the simple discount note and the simple interest note, we can calculate the proceeds and effective rates for each.
For the simple discount note, the interest is deducted upfront and the borrower receives the difference, or the proceeds. The interest on a $5,500 note at 6% for 18 months can be calculated as:
Interest = Principal × Rate × Time
Interest = $5,500 × 6% × 1.5 years
Interest = $495
The proceeds for the simple discount note can be calculated as:
Proceeds = Principal - Interest
Proceeds = $5,500 - $495
Proceeds = $5,005
The effective rate for the simple discount note can be calculated using the formula:
Effective Rate = Interest / Proceeds × 100%
Effective Rate = $495 / $5,005 × 100%
Effective Rate = 9.9%
For the simple interest note, the interest is calculated on the principal amount and added to the principal at the end of the term. The interest on a $5,500 note at 6% for 18 months can be calculated as:
Interest = Principal × Rate × Time
Interest = $5,500 × 6% × 1.5 years
Interest = $495
The total amount due at the end of the term for the simple interest note can be calculated as:
Total Due = Principal + Interest
Total Due = $5,500 + $495
Total Due = $5,995
The effective rate for the simple interest note can be calculated using the formula:
Effective Rate = Interest / Principal × 100%
Effective Rate = $495 / $5,500 × 100%
Effective Rate = 9.0%
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which point is a solution for the system of inequalities shown in the graph below?
Answer: The answer to your problem is choice b
Find all y-intercepts of the graph of
x² -10x + y² - 10y + 25 = 0.
Answer:
yjgdy
hgjg
hhjj
hggh
hhj
£11,000 was deposited in a savings account that pays simple interest. After 16 years, the account contains £17,160. Work out the annual interest rate of the account. Give your answer as a percentage (%) to 1 d.p.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 17160\\ P=\textit{original amount deposited}\dotfill & \pounds 11000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &16 \end{cases}[/tex]
[tex]17160 = 11000[1+(\frac{r}{100})(16)] \implies \cfrac{17160}{11000}=1+\cfrac{16r}{100}\implies \cfrac{39}{25}=1+\cfrac{4r}{25} \\\\\\ \cfrac{39}{25}=\cfrac{25+4r}{25}\implies 39=25+4r\implies 14=4r\implies \cfrac{14}{4}=r\implies \stackrel{\%\qquad }{\boxed{3.5=r}}[/tex]
Connor collected 80 stamps last year. This year he increased his collection by 20%. How many stamps are in his collection?
Answer:
96 stamps
Step-by-step explanation:
We know
Connor collected 80 stamps last year. This year he increased his collection by 20%.
80 stamps = 100%
100% + 20% = 120%
So, this year he collected 120% of the number of stamps from last year.
120% = 1.2
How many stamps are in his collection?
We take
80 times 1.2 = 96 stamps
So, there are 96 stamps in his collection.
Mr Lim and his family had a meal at a restaurant. Given that the price of food is subject to 6% of service tax. The total bill is RM190.80 including service tax. Calculate the service tax paid by Mr Lim.
Answer:
The service tax paid was:
0.06 * RM180 = RM10.80
Step-by-step explanation:
To calculate the service tax paid by Mr. Lim, we need to first find the amount of the bill before the service tax was added.
Let's call the original bill amount "x".
After the 6% service tax was added, the total bill became x + (0.06 * x) = RM190.80.
So we can set up the equation:
x + (0.06 * x) = RM190.80
Expanding the right side of the equation:
x + (0.06 * x) = 190.80
Combining like terms:
1.06x = 190.80
Solving for x:
x = 180
So the original bill amount before the service tax was added was RM180.
The service tax paid was:
0.06 * RM180 = RM10.80
