Answer:
£22.33
Step-by-step explanation:
calculate the cost of an album and a single track using simultaneous equations.
let a represent an album and s a single track , then
3a + 4s = 18.13 → (1)
2a + 5s = 13.93 → (2)
multiplying (1) by - 2 and (2) by 3 and adding will eliminate a
- 6a - 8s = - 36.26 → (3)
6a + 15s = 41.79 → (4)
add (3) and (4) term by term to eliminate a
0 + 7s = 5.53
7s = 5.53 ( divide both sides by 7 )
s = 0.79
substitute s = 0.79 into either of the 2 equations and solve for a
substituting into (1)
3a + 4(0.79) = 18.13
3a + 3.16 = 18.13 ( subtract 3.16 from both sides )
3a = 14.97 ( divide both sides by 3 )
a = 4.99
that is album costs £4.99 and single track £0.79
then cost to Charlotte is
cost = (4 × £4.99) + (3 × £0.79) = £19.96 + £2.37 = £22.33
The cost of 4 albums and 3 single tracks is £22.33
Let the cost of 1 album = £x
and let the cost of 1 single track = £y
Now, the cost of 3 albums and 4 single tracks = £3*x + £4*y
and cost of 2 albums and 5 single tracks= £2*x + £5*y
Given that,
£3*x + £4*y = £18.13 -------->(1)
£2*x + £5*y = £13.93 -------->(2)
Multiply (1) equation by 2 and (2) equation by 3 then solve for x and y.
On applying the substitution method we have,
x = £4.99 and y = £0.79
Now, we have to calculate the value of 4 albums and 3 single tracks.
It can be written as 4*x +3*y
£4*4.99 + £3*0.79 = £22.33
So, the cost of 4 albums and 3 single tracks is £22.33
This question is based on a linear equation in two variables. Here, we used two equations based on two variables and then solved them with the help of the substitution method.
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suppose the school parents club compited a cookbook. One company charges $750 to make a master copy and 25 for additional copy the total selling price depends on how many copies are ordered write a function rule and create a table of values to graph the value how much will you save per book by ordering 400 books instead of 100 books
The function rule for the total cost of the cookbook is C(x) = 750 + 25x, where x is the number of copies ordered.
# of Copies Ordered Total Cost
100 875
200 1000
300 1125
400 1250
If 400 copies are ordered instead of 100, the total cost would be $1250 instead of $875, saving $375 per book.
What is the measure of the base of the rectangle if the area
of the triangle is 32 ft²?
4 ft
Answer:
16
Step-by-step explanation:
16
Paying $40 for 6 pounds of chocolate.
Answer:
240$
Step-by-step explanation:
we multiply 40 with 6
(40×6)
imagine that two friends (heather and suzanne) are playing a video game where the player goes on quests to earn coins. the average number of coins earned on a quest is 2000. heather plays quite a bit, and goes on an average of 20 quests a day. suzanne doesn't play quite as much, and only goes on 5 quests a day. on a particular day, which person is less likely to record an average earning below 1500 coins?
When two friends are playing a video game where the player goes on quests to earn coins with an average number of 2000 coins earned in a quest, if one plays an average of 20 quests a day and other play 5 quests a day, none of them are likely to record an average earning below 1500 coins in a day.
Therefore the answer is both Heather and Suzanne are less likely to record an average earning below 1500 coins.
Here the average number of coins earned in a quest is not dependent on the number of quests played in a day. So for both Heather and Suzanne the average earning is to be 2000, so they are less likely to earn below 1500 coins.
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A website is selling packs of
playing cards for $2.07. The site
got the packs of playing cards at a
cost of $0.69. What is the mark-
up, as a percentage?
Answer:
66 2/3 % Markup
Step-by-step explanation:
1) Subtract the two numbers.
2.07 - 0.69 = 1.38
2) Divide the difference of the subtraction problem by 2.07, the value of the marked up cards.
1.38/2.07 = 2/3
3) Because percent means divided by 100, multiply 2/3 (0.6666...) multiplied by 100 as a fraction because x/100 x 100 = x.
66 2/3 % Markup
Help me please..30points!!!!
Answer:
Step-by-step explanation:
a) 10/18 · 9/17
5/9 · 9/17
5/17
b) 8/18 · 7/17
4/9 · 7/17
28/153
c) 10/18 · 8/17
5/9 · 8/17
40/153
Answer:
[tex]\textsf{a)} \quad \dfrac{5}{17}=29.4\%[/tex]
[tex]\textsf{b)} \quad \dfrac{28}{153}=18.3\%[/tex]
[tex]\textsf{c)} \quad \dfrac{40}{153}=26.1\%[/tex]
Step-by-step explanation:
Bag of 18 fruit drop sweets:
10 apple flavoured8 blackberry flavoured[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Part (a)The probability of the first sweet chosen being apple flavoured is:
[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]
Now there are 9 apple flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second apple flavoured sweet is:
[tex]\implies \sf P(apple)=\dfrac{9}{17}[/tex]
Therefore, the probability of both sweets being apple flavoured is:
[tex]\implies \sf P(apple)\;and\;P(apple)= \dfrac{10}{18} \times \dfrac{9}{17}=\dfrac{5}{17}[/tex]
Part (b)The probability of the first sweet chosen being blackberry flavoured is:
[tex]\implies \sf P(blackberry )=\dfrac{8}{18}[/tex]
Now there are 7 blackberry flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second blackberry flavoured sweet is:
[tex]\implies \sf P(blackberry )=\dfrac{7}{17}[/tex]
Therefore, the probability of both sweets being blackberry flavoured is:
[tex]\implies \sf P(blackberry )\;and\;P(blackberry )= \dfrac{8}{18} \times \dfrac{7}{17}=\dfrac{28}{153}[/tex]
Part (c)The probability of the first sweet chosen being apple flavoured is:
[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]
Now there are 9 apple flavoured sweets, 8 blackberry sweets, and a total of 17 sweets remaining, so the probability of choosing a blackberry flavoured sweet is:
[tex]\implies \sf P(blackberry)=\dfrac{8}{17}[/tex]
Therefore, the probability of the first sweet being apple flavoured and the second sweet being blackberry flavoured is:
[tex]\implies \sf P(apple)\;and\;P(blackberry)= \dfrac{10}{18} \times \dfrac{8}{17}=\dfrac{40}{153}[/tex]
Describe all the positive integers that would make (32)x greater than 39. Explain your reasoning
The positive integers that will make 32x greater than 39 are
2 3 4 5 6 ....... ∞
How to find the positive integersAn integer is a whole number that can be positive, negative, or zero and is not a fraction.
There are three types of integers, they are
ZeroPositive integers or natural numbersNegative integers or additive invers of natural numbersThe statement, given in the problem is written in equation form using the inequality > which represents greater than to be
32x > 39
The is solved as follows
32x > 39
x > 39 / 32
x > 1.219
hence the integers are 2 to infinity represented by the symbol ∞
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A triangle has sides of length 11cm, 10 cm, and 9cm.
Calculate the largest angle in the triangle.
Answer: In right angled triangle
Length of square of biggest side it's equal to length sum of square of two other sides
(11)² = (9)² + (10)²
121 = 81 + 100
121 = 181
So it is not a right angled triangle
Step-by-step explanation:
Mr. Tran mowed
1
4
of her lawn. Her on mowed
3
7
of it. Who mowed mot of the lawn? How much of the lawn till need to be mowed?
Mrs. Tran's son mowed more land than she and 9/28 of the land still need to be mowed.
let us convert all the fractions into equivalent fractions to make our calculations easy.
The land mowed by Mrs Tran = 1/4 x 7/7 = 7/28
The land mowed by her son = 3/7 x 4/4 = 12/28
Hence, we can clearly see that Mrs. Tran's son mowed more land than she.
The total land mowed by both of them = 7/28 + 12/28
= 19/28
The total land to be mowed = 1 - 19/28
= (28 - 19)/28
= 9/28
Hence, the land still to be mowed is 9/28.
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The complete question is -
Mrs. Tran mowed 1/4 of the lawn. Her son mowed 3/7 of it. Who mowed more? How much of the lawn still needs to be mowed?
Your task is to create a unique word problem that needs to be solved using a quadratic equation.
19. Eva is offered an interest rate of 5.28% for
her savings with simple compounding. What
is her equivalent rate with continuous
compounding?
[A] 0.0543 or 5.43%
[B] 0.0515 or 5.15%
ICI 0.5031 or 50.31%
[D] 0.3478 or 34.78%
E] 0.0508 or 5.08%
The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0515 or 5.15%, so option B is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Eva is offered an interest rate of 5.28% for her savings with simple compounding,
Here, P will be the same, the amount will be the same and the time will be the same,
The amount in simple compounding = The amount in continuous compounding
[tex]p(1 + r)^t = pe^{Rt}[/tex]
Here, R is the rate of interest for simple compounding,
[tex]1 + 0.0528 = e^R[/tex]
1.0528 = [tex]e^R[/tex]
R = ln 1.0528
R = 0.0515
Thus, the rate of interest for simple compounding is 5.15%
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The sequence 1, 3, 5, 7, 9, ..., is monotone
a) Decreasing
b) increasing
c) constant
d) oscillating
Answer: b) increasing
Step-by-step explanation: It seems evident that the sequence is made up of all the odd numbers.
[tex]\begin{gathered} \bold{a_1=1}\\ \bold{a_2=3=a_1+2}\\ \bold{a_3=5=a_2+2}\\ \bold{a_4=7=a_3+2} \\ \bold{a_n=a_{n- 1}+2}\end{gathered}[/tex]
As we can see, in the nth position (any position), we take the value of the previous position and add 2 to it. This leads us to conclude that the sequence is monotonic increasing since as we add 2 to the values, these grow up.
ABC and DEF are similar. Find the missing side length.
Answer:
DF = 24
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion.
[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )
[tex]\frac{DF}{4}[/tex] = [tex]\frac{36}{6}[/tex] = 6 ( multiply both sides by 4 )
DF = 4 × 6 = 24
you have sum([minutes of delay]) in your view. if aggregate measures is unchecked, what will the view show instead of sum([minutes of delay])?
It will show the individual values for each row in the view, rather than a sum of the values By time
When the aggregate measures option is unchecked, Tableau will display the individual values for each row in the view instead of totaling them up. This means that instead of showing the sum of the minutes of delay, the view will show the individual delay minutes for each row.
For example, if the view contains three rows with a delay of 10 minutes, 15 minutes and 20 minutes of time, the view will display 10, 15 and 20 instead of 45.
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suppose that you are rolling a six sided dice. let a = get a 3 what is p(ac)?
Take a six-sided dice for example.
If we let a, then a = 3.
Write about p (ac).
A six-sided die will obviously be rolled.
Obtaining a number fewer than three is required for letter A.The initials "AC" stand for "Anything which is not in A" on a die or "A-Complement".
A = 3 can be used to calculate a number less than 3 or a number greater than 3.
Taking into account that the possibilities 1, 2, 4, 5, and 6 are all in AC.
If we take the ratio of successful outcomes to overall outcomes, we have a chance.
P(AC) = 4/6 = 2/3
P(AC) is thus equal to 2/3.
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Please help me answer this question with a simple answer
Answer:
Subtract 2.5d from both sides.
Step-by-step explanation:
Subtract 2.5d from both sides.
7.5d = 2.5d
5d = 0
d = 0
What is 3x+2y(5) equal?
Answer:
3x+10y
Step-by-step explanation:
3x+2y(5) =
3x+2(5)y =
3x+2*5y = 3x+10y
For which value of x does each expression makes sense?
Answer:
x is less than 0
Step-by-step explanation:
Because the inside of the square root needs to be positive to make sense, the cube of -5x must be positive. The only way for a cube to be positive is if the base is positive, so x must be a negative number
a local ice cream shop has a parking lot with enough space for 18 cars. there are 7 cars in the parking lot right now.let x represent how many more cars can park in the lot. which inequality describes the problem?
The inequality describes the problem of a local ice cream shop has a parking lot with enough space for 18 cars is x + 7 ≤ 18
What is an Inequality?In mathematics, an inequality describes a relationship between two values of an algebraic expression that are not equal. “If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then, this relationship is called an inequality." For example, x>8 (x should be greater than 8).
We have, a local ice-cream shop has a parking lot with enough space.
The maximum number of cars will be parked in parking lot = 18.
At right now, the number of cars in parking lot= 7. Let assume that x be number of more cars can park in the lot. We have to express this in form of an Inequality. Total cars in parking lot = 7 + x but this number of cars cannot exceed the 18 , so x + 7 ≤ 18
Hence, required Inequality is x + 7 ≤ 18.
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What is the equation of a line with slope is -1/2 and passing through the p (-2, -1)
Answer:
y = -1/2x + 2
Which points have a distance of 3 units between them?
Select all that apply.
N=(1,4) and P=(1,1)
M=(−2,4) and N=(1,4)
R=(1,−2) and S=(−3,−2)
P=(1,1) and R=(1,−2)
P=(1,1) and Q=(3,1)
Answer:
Step-by-step explanation: The points that have a distance of 3 units between them are:
N=(1,4) and P=(1,1)
P=(1,1) and R=(1,-2)
P=(1,1) and Q=(3,1)
What is the slope of this line? Responses 1/3 1 third 2/3 2 over 3 −2/3 negative 2 over 3 −1/3
Answer:
2/3
Step-by-step explanation:
slope = rise/run
Start at point (0, -3).
Go up 2. That is a rise of 2.
Go right 3. That is a run of 3.
slope = rise/run = 2/3
Ticket to the zoo cot $25 for adult and $10 for children. The total ticket ale one day were $47,750. The number of children, c, who viited the zoo wa 270 more than 6 time the number of adult, a, who viited. Write and olve a ytem of equation to find the total number of viitor to the zoo that day
The total number of visitors to the zoo that day was 47,750, with 6,780 adults and 40,680 children.
Let a = number of adults
Let c = number of children
a + c = 47,750
c = 6a + 270
Substitute c in the first equation:
a + 6a + 270 = 47,750
7a = 47,480
a = 6,780
Substitute a in the second equation:
c = 6(6,780) + 270
c = 40,680
The total number of visitors to the zoo that day was 47,750, with 6,780 adults and 40,680 children.
The zoo was visited by 47,750 individuals. 40,680 of these visitors were youngsters under the age of 17 while 6,780 were adults 18 years and older.
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Choose by clicking the graph. Find Ltheta if sec theta = -13/5 and tan theta negative
The results of the two equations show that the tangent of a negative angle is always equal to its tan.
What if tan angle is negative?In trigonometric mathematics, this expression is known as the tangent of negative angle identity.Tan of negative angle identity is a mathematical relationship between the tangents of a negative and positive angle.Formulatan(-∅) = - tan∅
Proof : By using a geometrical approach in trigonometry, the mathematical relationship between the tangent of a negative angle and the tan of a positive angle is obtained.Construction of triangle with negative angle : Create the same triangle with a negative angle. As a result, QOR has a negative theta angle, represented by -∅.Write the tan of the negative angle in terms of the ratio of the lengths of the respective sides based on this information.tan (- ∅) = QR / OQ
The length of the opposite side will be yet the length of the adjacent side will be due to the building of the triangle with negative angle.=> tan (- ∅) = -y /x.
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completed the questions below
The slope of the line y = 10x + 3 is 10
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
Hence in the equation of the form y = 10x + c when compared with the equation of line in slope intercept form y = 10x + c
We can see that m which is the slope is 10
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for which of the three f-tests in a two-way anova do you collapse across the levels of the other factor(s) in computing the means?
The three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means both the A main effect and the B main effect.
What is meant by f-test?
In math, f-test refers to carry out the test for the equality of the two population variances.
Here we need to find in which of the three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means.
As per the definition of f-test, here we know that a two-way ANOVA do you collapse across the levels of the other factor has only two options that is main effect and interaction effect.
As we know that ANOVA separates the within group variance from the between group variance and the F-test is the ratio of the mean squared error between these two groups.
Therefore, in this one, both A and be has the main effect on each other.
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solve the equation by factoring x^2-4x=12
Answer:
x = - 2 , x = 6
Step-by-step explanation:
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
to factor, consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)
the factors are - 6 and + 2 , since
- 6 × 2 = - 12 and - 6 + 2 = - 4 , then
(x + 2)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 6 = 0 ⇒ x = 6
Which graph is not a function?
Please help me!!!
Answer:
First one
Step-by-step explanation:
The first is not a function ( the flower-looking one) ...it does not pass the 'vertical line test'
The test scores for
the 10 boys in a class
are
78
5879
45 39
The mean score for
the 5 girls in the class
is 8
Calculate the mean
for this class.
Answer: The mean score for this class is 17.13.
Step-by-step explanation:
Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249
Add the mean score for the girls: 249 + 8 = 257
Add up the number of students in the class: 10 + 5 = 15
Divide the total score by the number of students to find the mean: 257 / 15 = 17.13
What do you understand by mean and how many methods are there to find it ?
Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:
Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.
Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.
There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.
To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys. We have: 78+58+79+45+39 = 249
Next, let's add the mean score for the girls, which is 8.
So the total is now: 249 + 8 = 257.
Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.
Therefore, the mean score for this class is :
257/15 = 17.13.
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The mean score for this class is 17.13.
Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249
Add the mean score for the girls: 249 + 8 = 257
Add up the number of students in the class: 10 + 5 = 15
Divide the total score by the number of students to find the mean: 257 / 15 = 17.13
What do you understand by mean and how many methods are there to find it?
Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:
Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.
Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.
There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.
To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys.
We have: 78+58+79+45+39 = 249
Next, let's add the mean score for the girls, which is 8.
So the total is now: 249 + 8 = 257.
Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.
Therefore, the mean score for this class is :
257/15 = 17.13.
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Determine if x and y are inversely proportional. If applicable, find the constant of variation.
Answer:
x and y are inversely proportional , constant of proportion k = 30
Step-by-step explanation:
If x and y are inversely proportional then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
multiply both sides by y , then
k = xy
to check that k is constant use the ordered pairs from the table
(0.1, 300 )
k = 0.1 × 300 = 30
(0.5, 60 )
k = 0.5 × 60 = 30
(75, 0.4 )
k = 75 × 0.4 = 30
(100, 0.3 )
k = 100 × 0.3 = 30
thus x and y are inversely proportional with constant of proportion k = 30