The number of people who ride the bus is 70 students.
How to calculate the value?From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.
Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.
This will be illustrated as:
4/7 = 40/x
Cross multiply
4x = 40 × 7
4x = 280
Divide
x = 280/4
x = 70
Therefore there are 70 students.
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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?
Convert 50 degrees Fahrenheit to degrees celcius
10 degrees celsius
Explanations:The formula for converting temperature in degree Farenheit to degree Celcius is:
[tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(T_f-32) \\ \text{Where T}_c=\text{ temperature in degr}ees\text{ celcius} \\ T_f=\text{ temperature in degre}es\text{ Fahrenheit} \end{gathered}[/tex][tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(50\text{ - 32)} \\ T_c=\text{ }\frac{5}{9}\times18 \\ T_c=\text{ 5 }\times2 \\ T_c=10^0C \end{gathered}[/tex]Simplify the following expressions by using the properties of exponents. Assume none of the denominators is zero.
a^3 (2a^2 + 4bc^4)^ 0
The total value of the exponential expression is a³
What is Exponentiation ?
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Now, The given expression is :
a^3 (2a^2 + 4bc^4)^ 0
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Hence, The total value of the exponential expression is a³
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A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Decorations for the dance cost $120
the club is charging $10 per student that attends.
In the graph, the x axis is labelled with number of students and the y axis with amount of money collected
As they spend $120 for the decorations of the dance the starting point for the money raised is -120, upon charging 2 students the money they will get is 2 x 10 = 20
So the money raised will be
-120 + 20 = -100
The line will pass from point (0, -120) through (2, -100)
Therefore, graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100 is correct.
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Answer:
Step-by-step explanation:
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
Determine whether the graph represents a function.
The given graph representing function is a relation.
What is meant by relation and function?A function is a relation that states that there must be only one output for every input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the connection between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.(INPUT, OUTPUT): An ordered pair is depicted as (INPUT, OUTPUT):For the given question,
For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.
Thus, the graph shows the relation of the function.
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what is the 6th term in the sequence? f(1) = 10 f(n) = f(n-1) + 3
We will investigate the evaluation of recursive sequences.
A iterative sequences are categorized by two values i.e one value preceding and the current value. The current value is evaluated on the basis of the previous value. In other words the current value is a function of preceeding value or depends on it.
All iterative relations of a sequence are expressed mathematically by two values as follows:
[tex]\begin{gathered} f\text{ ( n ): Current nth term value} \\ f\text{ ( n - 1 ): preceeding/ previous value} \end{gathered}[/tex]A iterative relation is a unique mathematical relationship between the current term f ( n ) and the previous value given as follows:
[tex]\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( n ) = f ( n - 1 ) + 3}}[/tex]For this particular relationship the first term value is given as follows:
[tex]\textcolor{#FF7968}{n}\text{\textcolor{#FF7968}{ = 1, f ( 1 ) = 10}}[/tex]We will now start determining the terms in the sequence by plugging the respective term numbers ( n ) and use the mathematical relationship for the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 2,}} \\ f\text{ ( 2 ) = f ( 1 ) + 3} \\ f\text{ ( 2 ) = 10 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 2 ) = 13}} \end{gathered}[/tex]We have evaluated the 2nd term in the sequence as 13. We will repeat the above steps for all term numbers ( n = 3 , 4 , 5 , 6 ).
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 3,}} \\ f\text{ ( 3 ) = f ( 2 ) + 3} \\ f\text{ ( 3 ) = 13 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 3 ) = 16}} \\ \\ \text{\textcolor{#FF7968}{For n = 4,}} \\ f\text{ ( 4 ) = f ( 3 ) + 3} \\ \text{f ( 4 ) = 16 + 3} \\ \text{\textcolor{#FF7968}{f ( 4 ) = 19 }} \\ \\ \text{\textcolor{#FF7968}{For n = 5,}} \\ f\text{ ( 5 ) = f ( 4 ) + 3} \\ f\text{ ( 5 ) = 19 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 5 ) = 22}} \end{gathered}[/tex]And them lastly for the 6th term in the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 6,}} \\ f\text{ ( 6 ) = f ( 5 ) + 3} \\ f\text{ ( 6 ) = 22 + 3} \\ \text{\textcolor{#FF7968}{f ( 6 ) = 25}} \end{gathered}[/tex]Hence, the answer to the 6th term number is:
[tex]\textcolor{#FF7968}{25}[/tex]
The economy's real GDP was $100 billion in 2019 and $240 billion in 2020. Its
population was 15 million in 2019 and 15 million in 2020.
What is the growth rate of real GDP per capital from 2019 to 2020?
The growth of the real GDP per capita from 2019 to 2020 is 1.4.
How To calculate the growth rate of real GDP?It also calculates the amount of money spent on finished goods and services or the income generated from that production.GDP = private consumption + gross private investment + government investment + government spending + (exports – imports).GDP can be assessed in a variety of methods. The most popular techniques include Nominal GDP, Real GDP, Actual GDP, and Potential GDP.One of the key metrics used to assess the general health of a nation's economy and standard of life is its gross domestic product (GDP), which reflects economic growth and productivity. GDP growth rate is one approach to assess how well a nation's economy is doing. This rate indicates changes in the proportion of economic output over the course of a month, a quarter, or a whole year.Therefore, the formula to compute real GDP per capita = Real GDP / Population.
The real GDP in 2019 is $100B.
And the real GDP in 2020 is $240B.
Real GDP per capita of 2019 = 100B/15M. = 6666.6Real GDP per capita of 2020 = 240B/15M = 16000The growth rate of real GDP = current value - previous value / previous value
The growth rate of real GD P= 1.4Therefore, the growth of the real GDP per capita from 2019 to 2020 is 1.4.
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A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function Inverse of S is equal to the quantity t squared plus 3 times t minus 4 end quantity over the quantity t squared minus 6 times t plus 6 end quantity
Which equation represents the average sales each day for the real estate company?
An inverse function which represents the average sales each day for the real estate company is: D. S⁻¹ = (t + 4)/(t - 5).
How to determine equation?In order to determine equation which represents the average sales each day for the real estate company, we would factorize the numerator and denominator of the given inverse function as follows:
Numerator = t² + 3t - 4
Next, we would solve the quadratic equation by using the factorization method:
t² + 3t - 4 = t² + 4t - t - 4
t² + 4t - t - 4 = t(t + 4) - 1(t + 4)
t² + 4t - t - 4 = (t - 1)(t + 4)
Numerator = (t - 1)(t + 4)
For the denominator, we have:
t² - 6t + 5 = t² - 5t - t + 5
t² - 5t - t + 5 = t(t - 5) - 1(t - 5)
t² - 5t - t + 5 = (t - 1)(t - 5)
Denominator = (t - 1)(t - 5)
Now, we would rewrite the inverse function as follows:
S⁻¹ = Numerator/Denominator
S⁻¹ = (t - 1)(t + 4)/(t - 1)(t - 5)
S⁻¹ = (t + 4)/(t - 5)
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given angle <afb and <rst are supplementary and the m<afb = 7x - 18 and the m<rst = 72 - 2x what is the value of x? what is the m<afb and m<rst be sure to show your work and all three answers.
The most appropriate choice for supplementary angle will be given by-
x = 25.2°
∠AFB = 158.4°
∠RST = 21.6°
What is supplementary angle?
Angle is formed when two straight lines meet at a common point.
The common point is the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if their sum is 180°
Here,
∠AFB = 7x - 18
∠RST = 72 - 2x
Sum = 7x - 18 + 72 - 2x
= 5x + 54
By the problem,
[tex]5x +54=180\\5x = 180-54\\5x =126\\x= \frac{126}{5}\\x = 25.2[/tex]
∠AFB = [tex]7 \times 25.2 -18\\[/tex]
= [tex]176.4 - 18\\[/tex]
= [tex]158.4^{\circ}[/tex]
∠RST =
[tex]72 - 2\times 25.2\\72 - 50.4\\21.6^{\circ}[/tex]
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6 less than the number x
-3/16, 7/4, -3/8 write in order from least to greatest
a We have fractions in order to order from least to greatest we will convert the fractions into decimal number
[tex]-\frac{3}{16}=-0.1875[/tex][tex]\frac{7}{4}=1.75[/tex][tex]-\frac{3}{8}=-0.375[/tex]as we can see the least number is -3/8 then -3/16 and the greatest number is 7/4
[tex]undefined[/tex]evaluate x=5 and y=7
y2-x/y+3x
The answer to the given expression is 2
How to solve variables?To "solve" or "isolate" a variable is to place it on its own side of the equation.
All other variables or constants should be moved to the opposite side of the equation using inverse operations. The operations must be applied to both sides of the equation in order to maintain the equation's balance.
Given : x = 5 and y = 7
To find : [tex]\frac{y^{2} - x }{y + 3x}[/tex]
When we substitute the values mentioned above in this above expression we get;
[tex]\frac{7^{2}- 5 }{ 7+ 3X5}[/tex]
⇒ [tex]\frac{49 - 5}{ 7 + 15}[/tex]
⇒ [tex]\frac{44}{22}[/tex]
On dividing it with 22 we get
[tex]\frac{44}{22}[/tex] = 2
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You have been given $10,000 to invest. Safe investments, like certificates of deposit, pay about 5.5% interest. The stock market is much riskier but pays about 12%. If you would like to earn about 10% a year on these investments, how much would you invest in CDS and how much should you invest in stocks?
will give brainliest ty
Answer:
Let x = amount in low risk account, then 10000-x is amount invested in high risk account. To earn 10% of 10000:
(.10)(10000) = (.055)x + .12(10000-x)
1000 = 1200 -.045x
x = 4444.44 in low risk and 5555.56 in high risk
Linh buys $11.23 worth of groceries and pays for them with a $20 bill.List her change using the smallest number of coins and bills?
Given: Linh buys $11.23 worth of groceries and pays for them with a $20 bill.
So, the change will be = 20 - 11.23 = $8.77
Holly ate one more brownie, then Tori from the same small pan. Write two equivalent fractions that describe how much Holly eight.
Holly ate two [tex]\frac{1}{6}[/tex] fractions.
Holly ate 1 more brownie, then Tori
= 1+2
= 3
She ate [tex]\frac{3}{9}[/tex] fraction
Two equivalent fractions = [tex]\frac{3}{9} = 2x[/tex]
[tex]x = \frac{1}{6}[/tex]
Holly ate two [tex]\frac{1}{6}[/tex] fractions.
What are Fractions?
Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the bottom part represents the denominator, and the top part the numerator. This article's focus is on going to learn the meaning of fractions in mathematics, different sorts of fractions, how to convert fractions to decimals, and a ton of problems that have been solved and well explained.
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Which choices are equivalent to the fraction below? Check all that apply.330327O A. 357O B. 34O c. 27D. 33
Given:
We have given fraction
[tex]\frac{3^{30}}{3^{27}}[/tex]Required:
We have to find the required data which is equal to above fraction solution.
Explanation:
In the above fraction we have same base in numerator and denominator and hence,
when the base is same power are added.
[tex]=3^{30-27}\text{ =3}^3[/tex]Required answer:
Option d is correct.
which is equal to our calculated answer.
triangle DEF is rotated 90 to the right to format the triangle with the side lengths shown below
Problem
Solution
For this case we can conclude that:
DE = r
DF= s
EF= t
Match the terms (picture)
Answer:
Match that i have the step by step explanations
Step-by-step explanation:
A, F, C, D, E, F, B
completed the chart for ordered pairs .Using the equation* reduce all fractions to the lowest terms.Given equation: 10 x- 8y =16x tea chart : __,0,2,__y tea chart: 0,__,__,4fil in the blanks
-When y = 0 :
10*x -8*0 = 16 (Replacing y=0)
10x = 16 (Multiplying)
x = 16/10 (Dividing on both sides of the equation by 10)
x= 8/5 (Simplifying)
- When x= 0:
10*0 -8*y = 16 (Replacing x=0)
-8y = 16 (Multiplying)
y= 16/(-8) (Dividing on both sides of the equation by -8)
y= -2 (Dividing)
- When x= 2
10*2 -8*y = 16 (Replacing x=2)
20 - 8y = 16 (Multiplying)
20 = 16 + 8y (Adding 8y to both sides of the equation)
20 - 16 = 8y (Subtracting 16 from both sides of the equation)
4 = 8y (Subtracting)
4/8 = y (Dividing on both sides of the equation by 8)
1/2 = y (Simplifying)
- When y= 4
10*x -8*4 = 16 (Replacing y=4)
10 x - 32 = 16 (Multiplying)
10x = 32 + 16 (Adding 32 to both sides of the equation)
10x=48 (Adding)
x = 48/10 (Dividing on both sides of the equation by 10)
x=24/5 (Simplifying)
So, the complete chart would be:
x tea chart : 8/5,0,2, 24/5
y tea chart: 0,-2,1/2,4
I rlly need help on this problem-
Two factors are multiplied and their product is 34.44. One factor is a whole number. What is the least number of decimal places in the other factor?
The least number of decimal places in the other factor is 2
What is a factor?A factor simply means the number that can b multiplied with another number to get the original number.
Based on the question asked, lat the whole number be represented as 2. In this case the multiplication will be:
= 2 × 17.22
=34.44
In this case, one can see that 17.22 has 2 decimal places.
Therefore, the correct option is 2.
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Help plllllesessssssssssssssssssssssssssssssssssssssssssssssssss
Answer: 8 + 7x
Step-by-step explanation:
The perimeter is the same as all the side lengths added together. We will set up an expression, then simplify it by combining like terms.
(4 - x) + (7x - 1) + (6x + 13) + (-8 - 5x)
4 - x + 7x - 1 + 6x + 13 - 8 - 5x
4 - 1 + 13 - 8 - x + 7x + 6x - 5x
8 + 7x
The age of children in kindergarten on the first day of school is uniformly distributed between 5 and5.76 years old. A first time kindergarten child is selected at random. Round answers to 4 decimalplaces if possible.a. The mean of this distribution isb. The standard deviation isC. The probability that the the child will be older than 5 years old?d. The probability that the child will be between 5.4 and 5.6 years old ise. If such a child is at the 53rd percentile, how old is that child?years old.CalculatorScratchwork Area
Given the interval of the distribution as
[tex]5-5.76[/tex]a) To find the mean, we will calculate the mid-value of the interval, this is shown below
[tex]\operatorname{mean}=\frac{5+5.76}{2}=\frac{10.76}{2}=5.38[/tex]Hence, the mean is 5.38
b) To find the standard deviation
[tex]\begin{gathered} SD=\sqrt[]{\frac{(b-a)^2}{12}} \\ b=5.76 \\ a=5 \\ SD=\sqrt[]{\frac{(5.76-5)^2}{12}} \\ =\sqrt[]{\frac{0.76^2}{12}}=0.2194 \end{gathered}[/tex]Hence, the standard deviation is 0.2194
c) The probability that the child will be older than 5 years will be
[tex]P(older\text{ than 5 years)=}\frac{5.76-5}{5.76-5}=\frac{0.76}{0.76}=1.0[/tex]Hence, the probability that the child will be older than 5 years is 1.0
d) The probability that the child age is between 5.4 and 5.6 years old will be
[tex]P(\text{ between 5.4 and 5.6 years old)=}\frac{5.6-5.4}{5.76-5}=\frac{0.2}{0.76}=0.2632[/tex]Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632
e) If the child is at the 53rd percentile, the age of the child will be
[tex]\begin{gathered} At\text{ 53rd percentile the age}\Rightarrow5+\frac{53}{100}(5.76-5) \\ =5+0.53(0.76) \\ =5.4028 \end{gathered}[/tex]Hence, at the 53rd percentile, the age of the child is 5.4028 years old
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How many times larger is (1.064 x 101) than (7 x 10−1)?
0.152
15.2
6.58
7.448
Answer:
the correct answer is 15.2
Solve the linear system using the elimination method. Type youranswer as an ordered pair in the form (#,#). 6x + 5y = -15-2x – 3y = 17
1) Solving that linear system using the elimination method, we'll proceed this way.
1.1 Choose one variable to be canceled out firstly. Let's choose the x variable:
6x + 5y = -15
-2x -3y= 17 Multiply this whole equation by 3
6x + 5y = -15
-6x -9y= 51 Add both equations
----------------------
0 -4y =36 Divide both sides by -4
y = -9
2) Now let's plug into any equation, usually the one with smaller numbers y= -9
-2x -3(-9) = 17
-2x +27 = 17 Subtract 17 from both sides
-2x =17-27
-2x = -10 Divide both sides by -2
x= 5
3) So the solution is (5, -9)
-
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Answer:
Printer B prints the fastest
775,710 teenagers voted for their favorite singer on a TV show. Each singer received the exact same number of votes. How many singers could there have been?a) 5b) 2c) 6d) 9
There could have been 2,5,6, and 9 singers
1) Regarding 775,710 as an even number then for sure there could have been 2 singers on this TV Show
[tex]775710\colon2=387,855[/tex]2) On the other hand, 775710 is also divisible by 5, for its last number is 0. So there could also have been 5 singers.
[tex]775710\colon5=155,142[/tex]3) This number of teenagers can also be divided by 6 (for it is divisible by 2 and by 3) and by 9 as well ( the sum of the digits of 775710, 7+7+5+7+1+0=27 is also divisible by 9).
Hence, there could have been 2,5,6, and 9 singers since 775,710 can be divided exactly by 2,5,6, and 9.
2. Maryse went for a bike ride. She rode at a constant speed, an she traveled 7 miles in one hour.Maryse wrote the equation y=7x to model her bike ride, where x is the time Maryse spent riding,and y is the distance she traveled.a. Maryse uses her equation to estimate that she rode 14 miles in the first two hours of her trip.Did she use her equation correctly? Explain why or why not. Ensure to write the equation withthe appropriate numbers plugged in.b. Maryse uses her equation to predict that she would travel 40 miles if she rode for four hours.Did she use her equation correctly? Explain why or why not.
ANSWER
1.) YES! Maryse used her equation correctly.
2.) NO! Maryse did not use her equation correctly.
EXPLANATION
Given:
A bike ride model: y = 7x
where:
1). x is the time Maryse spent riding,
2). y is the distance she traveled
Now, she rode 14 miles in the first two hours of her trip
That is:
y = 7x
where y = 14 miles and x = 2 hours
14 = 7(2)
14 = 14
She indeed used her equation correctly.
When she predicted that she would travel 40 miles if she rode for four hours.
That is:
y = 7x
where y = 40 miles and x = 4 hours
[tex]\begin{gathered} 40\text{ }\ne\text{ 7\lparen4\rparen} \\ 40\ne28 \end{gathered}[/tex]Hence, She indeed used her equation correctly in part one but she did not use her equation correctly in part two.
The graph shows the number of each kind of book in Hero's personal library. A book is chosen randomly.
What is the probability that the book chosen is an adventure?
20. A room is 24 feet long and 15 feet wide. How much will it cost to cover the floorwith carpet costing $36 a square yard if an extra 4 square yards must be purchasedfor matching?Answer
At first, we will change the feet to the yard because the cost of carpet is per square yard
Since 1 yard = 3 feet, then
Divide each dimension by 3 to change it from feet to yard
Since the length of the room = 24 feet, then
The length of the room = 24/3 = 8 yards
Since the width of the room = 15 feet, then
The width of the room = 15/3 = 5 yards
The rule of the area of the rectangle is
Area = Length x width, then
The area of the room = 8 x 5 = 40 square yards
Since we will add extra 4 square yards to it, then
The total area needs to cover = 40 + 4 = 44 square yards
Since the cost of 1 square yard = $36, then
Multiply the area by the cost to find the cost of the carpet
The total cost = 44 x 36 = 1584
The cost of the carpet is $1584
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.60 and the cost of a large greeting card is $4.05. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?Total cost, 5 small greeting cards and 4 large greeting cards: Total cost, x small greeting cards and y large greeting cards:
From the given question, we have the following parameters
Cost of a small greeting card = $1.60
The cost of a large greeting card = $4.05.
Cost of 5 small greeting cards = 5(1.60)
Cost of 5 small greeting cards = $8.00
Cost of 4 large greeting cards = 4(4.05)
Cost of 4 large greeting cards = $16.2
Cost of 5 small and 4 large = $8.00 + $16.2
Cost of 5 small and 4 large $24.2
Hence it would cost $24.2 to get 5 small greeting cards and 4 large greeting cards
Similarly;
Cost of x small greeting cards = 1.60x
Cost of y large greeting cards = 4.05y
Cost of small greeting cards and y large greeting cards = 1.60x + 4.05y
Hence it would cost $(1.60x + 4.05y) to get x small greeting cards and y large greeting cards
Use the formula for nCr to evaluate the expression. 10c3/6c4
SOLUTION
The given expression is
[tex]\frac{^{10}C_3}{^6C_4}[/tex]Recall the formula for combination
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Solving the given expresssion
[tex]\frac{^{10}C_3}{^6C_4}=\frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!}[/tex]This further gives
[tex]\begin{gathered} \frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!} \\ =\frac{10!}{7!3!}\div\frac{6!}{2!4!} \\ =\frac{10!}{7!3!}\times\frac{2!4!}{6!} \end{gathered}[/tex]This further gives
[tex]\begin{gathered} =\frac{10\times9\times8\times7!}{7!\times3\times2!}\times\frac{2!4!}{6\times5\times4!} \\ =\frac{10\times9\times8}{6\times5\times3} \\ =8 \end{gathered}[/tex]Therefore the solution is 8