Answers
We are given the recipes of Grandma and Betty Potter box.
We are asked to find out which of them makes more cookies per cup of chocolate chips.
Let us find the unit rate for both of them and compare which is greater.
Grandma:
She uses 1 1/2 cups of chocolate chips to make 24 cookies.
The unit rate is
[tex]\frac{24}{1\frac{1}{2}}=\frac{24}{\frac{3}{2}}=24\times\frac{2}{3}=16[/tex]So the unit rate is 16 cookies per chocolate chip.
Betty Potter box:
60 cookies are made using 3 chocolate chips.
80 cookies are made using 4 chocolate chips.
200 cookies are made using 10 chocolate chips.
The unit rate is
[tex]\begin{gathered} \frac{60}{3}=20 \\ \frac{80}{4}=20 \\ \frac{200}{10}=20 \end{gathered}[/tex]So the unit rate is 20 cookies per chocolate chip.
As you can see, the recipe of Better Potter box makes more cookies per cup of chocolate chip.
Related Questions
Louis and Jenny each wrote an equation to represent the graphed linear function. Louis’s answer is y=2x. Jenny’s answer is y=x+2. Which student is correct?
Answers
Concept
First, find the slope of the line, and secondly use a slope-intercept form of the equation to find the equation of the line.
Step 1: find the slope
From the graph, choose two coordinates at the intercept
( 0, 2 ) and ( -2, 0 )
x1 = 0
y1 = 2
x2 = -2
y2 = 0
Substitute the values in slope equation
[tex]\begin{gathered} \text{Slope m = }\frac{rise}{\text{run}}\text{ }=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Slope = }\frac{0-2}{-2-\text{ 0}} \\ \text{m = 1} \end{gathered}[/tex]Step 2: Find the intercept c
The intercept on the y-axis is c = 2
Step 3: Write the equation of a line in slope-intercept form
y = mx + c
Step 4: substitute the values of m and c to find the equation
y = 1(x) + 2
y = x + 2
Final answer
y = x + 2 Jenny's is correct
f(1)=-12 and f(n)=2f(n-1) then find the value of f(6).
Answers
Notice that from the definition of f(n):
[tex]f(6)=2f(5)=2(2f(4))=2(2(2f(3)))=2(2(2(2f(2))))=2(2(2(2(2f(1)))))\text{.}[/tex]Therefore:
[tex]f(6)=2^5f(1)=2^5(-12)=32(-12)=-384.[/tex]Answer:
[tex]f(6)=-384.[/tex]help me please if you can A.(0, 3)B. (-1, 5)C.(1, 1.5)
Answers
Answer:
A. (0, 3)
C. (1, 1.5)
Explanation:
A point is a solution to the system if it satisfies both inequalities.
So for each option, we get:
Replacing (x, y) = (0, 3)
y ≥ -2x + 3
3 ≥ -2(0) + 3
3 ≥ 3
y ≤ -x² - x + 4
3 ≤ -0² - 0 + 4
3 ≤ 4
Since both inequalities are satisfied, (0, 3) is a solution.
For (x, y) = (-1, 5)
y ≥ -2x + 3
5 ≥ -2(-1) + 3
5 ≥ 2 + 3
5 ≥ 5
y ≤ -x² - x + 4
5 ≤ -(-1)² - (-1) + 4
5 ≤ -1 + 1 + 4
5 ≤ 4
Since 5 is not lower than 4, (-1, 5) is not a solution
For (x, y) = (1, 1.5)
y ≥ -2x + 3
1.5 ≥ -2(1) + 3
1.5 ≥ -2 + 3
1.5 ≥ 1
y ≤ -x² - x + 4
1.5 ≤ -(1)² - (1) + 4
1.5 ≤ -1 - 1 + 4
1.5 ≤ 2
Since both inequalities are satisfied, (1, 1.5) is a solution.
Therefore, the answers are
A. (0, 3)
C. (1, 1.5)
find the area of the figure below, composed of a rectangle with two semicircles removed.
Answers
This is a composite shape composed of a rectangle with two semicircles removed. The area will be calculated by subtracting the area of the two semicircles from the area of the rectangle
The area of a rectangle is given by:
[tex]\begin{gathered} Area(rectangle)=length\cdot width \\ length=12 \\ width=6 \\ Area(rectangle)=12\cdot6=72 \\ Area(rectangle)=72 \end{gathered}[/tex]The area of the two semicircles is given by:
[tex]\begin{gathered} Area(2semicircles)=2(\frac{1}{2}\pi r^2) \\ Area(2semicircles)=\pi r^2 \\ r=\frac{diameter}{2}=\frac{6}{2}=3 \\ Area\mleft(2semicircles\mright)=\pi\cdot3^2=3.14\cdot9=28.26 \\ Area\mleft(2semicircles\mright)=28.26 \end{gathered}[/tex]Therefore, the area of the figure is:
[tex]\begin{gathered} Area(figure)=Area(rectangle)-Area(2semicircles) \\ Area(figure)=72-28.26 \\ Area(figure)=43.74\approx43.7 \\ Area(figure)=43.7 \end{gathered}[/tex]According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 70 received emails.
(a)
What is the expected number of these emails that are tracked?
(b)
What are the variance and standard deviation for the number of these emails that are tracked? (Round your answers to three decimal places.)
Var(x)
=
=
Answers
Using the binomial distribution, the measures are given as follows:
a) Expected value: 28.
b) Variance of 16.8 and standard deviation of 4.099.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Hence, in the context of this problem, the values of these parameters are given as follows:
p = 0.4, n = 70.
The expected value of the distribution is calculated as follows:
E(X) = np.
Hence:
E(X) = 70 x 0.4 = 28.
The variance of the distribution is calculated as follows:
V(X) = np(1 - p) = 70 x 0.4 x 0.6 = 16.8.
The standard deviation of the distribution is calculated as follows:
sqrt(V(X)) = sqrt(16.8) = 4.099.
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6+|2x-11|=-37
Solve for x
Answers
Answer:
X=16 and X=21
Step-by-step explanation:
6 + 2x-11 = -37
-6 -6 2x-11 =-43
+11 +11 2x =32
x=16
6+ 2x- 11 = 37
2x-11=31
+11 +11 2x=42
x =21
A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
please refer to the image
Answers
The required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
What is the equation?the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
According to the question,
6x + 5y = 28 - - - - (1)
2x + 3y = 14 - - - - (2)
Solving equations 1 and 2 by substitution method we get,
x = 7/4 = and y = 7/2
Thus, the required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
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(4 to the 3rd power * 4 to the 6 power)to the 5th power
Answers
hello
if i'm right, what you're trying to ask is
the sum of three consecutive integers is 219. find The largest of the three integers.
Answers
Let n be the lesser number of the three. Therefore,
[tex]n+(n+1)+(n+2)=219[/tex]Solving for n,
[tex]\begin{gathered} \Rightarrow3n+3=219 \\ \Rightarrow3n=216 \\ \Rightarrow n=72 \end{gathered}[/tex]Then, the three numbers are 72, 73, and 74. The answer is 74
anumeha mows lawns she charges an initial fee and constant fee for each hour of work
Answers
Given the function:
[tex]F(t)=6+12t[/tex]Where F represents Anumeha's fees (in dollars) for working t hours. The initial fee can be calculated for t = 0:
[tex]F(0)=6+12\cdot0=6[/tex]So the constant fee is $6. Now, we need to calculate how much does she charges each hour. We can calculate the values at t = 1, t = 2, and t = 3:
[tex]\begin{gathered} F(1)=6+12\cdot1=18 \\ F(2)=6+12\cdot2=30 \\ F(3)=6+12\cdot3=42 \end{gathered}[/tex]As we can see, there is a constant increment of $12 for each hour. Then, Anumeha charges $12 for each hour of work.
Let S be the universal set, where: S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } Let sets A and B be subsets of S , where: Set A = { 2 , 5 , 9 , 11 , 12 , 14 , 15 , 17 , 18 } Set B = { 4 , 7 , 8 , 9 , 10 , 12 , 15 , 17 , 18 , 19 , 20 } Find the following: LIST the elements in the set ( A ∪ B ): ( A ∪ B ) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( A ∩ B ): ( A ∩ B ) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
Answers
The elements that are in ( A ∪ B ) = { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}
The elements of the set that are in ( A ∩ B ) = {9, 12, 15, 17, 18 }
What is a the union of a set?This is the term that is used to refer to all of the elements that are contained in a two or more sets which are a subset of the Universal set.
In this case, the union of the set is given as the elements in both A and B written together as { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}. All of these values are in A and B.
What is the intersection of a set?This is the term that is used to refer to all of the values that would appear in the two sets that are in the subset of the universal set.
Here we have the value of A ∩ B = {9, 12, 15, 17, 18 }
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please help me with this question
Answers
The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x
Given,
The cost of a convention center to host an event = $300 + $45 per person attending
Number of attendees = x
We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.
Here,
Total cost for the event = Fixed cost + cost per person attending x number of person
Total cost = 300 + 45 × x
Total cost = 300 + 45x
Now,
The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x
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Solving a present makes your problem using a system of linear equations
Answers
Answer:
Explanation:
Jamal built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box.
Answers
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will first calculate the area of the base, the area of the short side and the area of the longest side, then we have:
Base area=6 in * 14 in=84 in^2
Short side area=8 in * 6 in = 48 in^2
Longest side area=8 in * 14 in=112 in^2
Total surface area=Base area+ 2(Short side area) + 2(Longest side area)
Total surface area=84 in^2+ 2(48 in^2) + 2 (112 in^2)
Total surface area=84 in^2+ 96 in^2 + 224 in^2
Total surface area=404 in^2
Finally we obtain that the total surface area in square inches of the toy box is 404 in^2.
Please help me asap with both I’ll mark you brainly
Answers
1. The scholar made a mistake in the last step
where he said x=3.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS
[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]
Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n
[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]
FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.
I HOPE THIS HELPS.
Finding the Midpoint of a Line
Segment
To find the midpoint, M, of AB we can use
formula for finding point C. This works
because the M lies along AB and divides it in
a fixed ratio. So, if the midpoint of AB is point M, what must the ratio of a : b be? Since we know the ratio of a to b, we can substitute the values you wrote above back into the formula for finding a point along a line segment.
Answers
Define table represents grouped frequency distribution of the number of hours found computer per week for49 students. What is the value of the upper class limit of the fifth class
Answers
Sample unit: students
Sample size: 49
Variable: number of hours spent on the computer per week
There are 5 classes. The 5th class (the last one) of the table is:
14.0 - 17.4
Its upper-class limit of the 5th class is 17.4 hours
Sally wishes to purchase an IPhone 12. the price of the item is $849. the amount of money she save's per month is $70. The amount of money Sally already have's is $17. , , , : write your function and define your variables. your function should be in a slope-intercept form. what is ()input = number of months. and ()output = amount of money you need :: complete your input/output tabel. select 6 values for your input (). They can be consistent (, , , , , , ) Whatever the case, it should match your function. Substitute those values into your function to solve for your output () : create your graph. Clearly label your - and - axis and use an appropriation scale. Use the ordered pair from your input/output table to place on the graph. Connect your points with a straight line. : 1. how long will it take you to reach your goal and purchase your item? 2. looking at your data (table and graph) what is one observation you can make? 3. if you double your savings each month, how does this affect the time it takes to reach your goal amount? 4. how do you know your equation is a function?
Answers
Question 1 of 10 - What is the value of the expression below when d= 5 and m = -2? d? + | dm|
Answers
Note the absolute value of any negative value is positive.
The Shoe Outlet bought boots for $60 and marks up the boots 55% on the selling price. What is the selling price of the boots?
Answers
If the markup is of the 55%, then the selling price will be the 155% of the original price, this means that the selling price is:
S = $93.
What is the selling price of the boots?If the original price is P, and the markup is given by a percentage X, then the selling price of the product will be:
S = P*(1 + X/100%).
In this case, the original price is $60 and the mark up is of 55%, then we have:
P = $60
X = 55%.
S = $60*(1 + 55%/100%) = $60*(1 + 0.55) = $93
The selling price is $93.
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35* 35. Which of the following values for r suggests that one variable causes another? A. -0.7 B. O C. 0.9 D. None of the above
Answers
The correlation coefficient r indicates if two variables are or not dependent. If r is close to 1, then one variable causes the other one. From the options, a value of 0.9 suggests that one variable causes another
give the answer as a mixed number and as an improper fraction (number 1)
Answers
Answer:
Jossie has filled 59/30 of the 3 baskets.
Step-by-step explanation:
If Jossie has filled 3/5 of one, 7/10 of another, and 2/3 for the last one. The proportion of the total baskets:
[tex]\frac{3}{5}*\frac{2}{2}+\frac{7}{10}+\frac{2}{3}=\frac{6}{10}+\frac{7}{10}+\frac{2}{3}[/tex]Compute.
[tex]\frac{13}{10}+\frac{2}{3}=\frac{39+20}{30}=\frac{59}{30}[/tex]Jossie has filled 59/30 of the 3 baskets.
please solve quickly and give solution first then explain if possible
Answers
Solution
[tex]undefined[/tex]The final answer
[tex]x=10[/tex]The width of a rectangle measures (8u - 2v) centimeters, and its length meas(5u +9v) centimeters. Which expression represents the perimeter, in centimof the rectangle?
Answers
The perimeter of a rectangle is given by two times the length plus two times the width, so we have:
[tex]\begin{gathered} P=2L+2W\\ \\ P=2(5u+9v)+2(8u-2v)\\ \\ P=10u+18v+16u-4v\\ \\ P=26u+14v \end{gathered}[/tex]Therefore the perimeter's expression is 26u + 14v
Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.
Answers
1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.
2. Their combined monthly totals are:
Income = $3,356.
Expenses = $3,111.
3. Their monthly net cash flow is $245.
What is the net cash flow?The net cash flow is the cash surplus after paying all operating costs.
The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.
For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.
1 year = 52 weeks
1 month = 4.33 weeks (52/12)
Monthly Income:
Corbie = $2,750
James = $606 ($280 x 26/52 x 4.333)
Total income = $3,356
Monthly Expenses:
Rent = $925
Utilities = $325
Phones = $180
Groceries = $520 ($120 x 4.33)
Gas = $195 ($45 x 4.33)
Tuition = $100 ($600 x 2)/12
Incidentals = $866 (200 x 4.33)
Total expenses = $3,111
Net Cash Flow = $245 ($3,356 - $3,111)
Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.
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a survey of 240 households.91 had a dog. 70 had a cat. 31 had a cat and dog. 91 had neither a cat or a dog and did not have a parakeet. 7 had a cat, a dog and a parakeet. how many had a parakeet only?
Answers
A total of 240 households participated in the survey.
91 of then had neither a cat, a dor or a parakeet.
Then, 159 of them had at least one animal.
7 of then had a cat, a dog and a parakeet.
Then, 152 of them had one or two animals between a cat, a dog and a parakeet.
31 of them had a cat and a dog.
Then, 121 of then had a dog only, a cat only, a dog and a parakeet, a cat and a parakeet or a parakeet only. Between these, we want to find the ones who had a parakeet only. Only 91 - 31 = 60 of these 121 households must had at least a dog and only 70 - 31 = 39 of these had at least a cat.
Therefore, the number of households that had a parakeet only is 121 - 60 - 39 = 22
If it costs $1.50 for a pack of Starbursts at ShopRite, how much will 5 packs cost?
Answers
Answer : $7.5
1 pack of starbursts cost $1.50 at shoprite.
How much will 5 packs cost
Let the cost in dollars of 5 packs of starbursts be x
1 pack will cost $1.50
5 packs will cost $x
Mathematically,
1 pack ---------------- $1.50
5 packs -------------= $x
Cross multiply
1 * x = 5 x 1.50
x = $7.5
Hence, 5 packs of starbursts would cost $7.5
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chefwants to make 370 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Answers
Assuming these are volume percentages and the volumes don't change when you mix them, we can calculate this using a system of equations.
But first we need to identify each equation and variable.
let x be the volume of 7% vinegar used and y be the volume of 12% vinegar used.
The total volume is the sum of those and it must be equal to 370 mL, so:
[tex]x+y=370[/tex]The amount of vinegar in the x volume of 7% vinegar can be calculated by multiplying x by the 7%, that is, by 0.07:
[tex]0.07x[/tex]Similarly, the amount of vinegar in y is:
[tex]0.12y[/tex]So, the total amount of vinegar after the mixture is:
[tex]0.07x+0.12y[/tex]Since the percentage of the final mixture is 8%, the amount after the mixture can also be calculated by taking 8% of the final volume of 370mL, that is:
[tex]0.08\cdot370=29.6[/tex]The two ways of calculating the amount of vinegar in the mixture must be the same, so we have got our second equation:
[tex]0.07x+0.12y=29.6[/tex]So, the system of equations is:
[tex]\begin{gathered} x+y=370 \\ 0.07x+0.12=29.6 \end{gathered}[/tex]We can solve this by substitution:
[tex]\begin{gathered} x+y=370 \\ x=370-y \end{gathered}[/tex]Thus:
[tex]\begin{gathered} 0.07x+0.12y=29.6 \\ 0.07(370-y)+0.12y=29.6 \\ 0.07\cdot370-0.07y+0.12y=29.6 \\ 25.9+0.05y=29.6 \\ 0.05y=29.6-25.9 \\ 0.05y=3.7 \\ y=\frac{3.7}{0.05} \\ y=74 \end{gathered}[/tex]And, going back to the first equation:
[tex]\begin{gathered} x=370-y \\ x=370-74 \\ x=296 \end{gathered}[/tex]. Estimate the area of a parallelogram with a base of 3 ¼ yards and a height of 5 ½ yards.
Answers
We are given the dimensions of a parallelogram and are asked to estimate its area
Recall that the area of a parallelogram of base b and height h is given by the formula
[tex]A=b\cdot h[/tex]So the area of the parallelogram would be
[tex]3\frac{1}{4}\cdot5\frac{1}{2}[/tex]as 3 1/4 and 5 1/2 are mixed numbers, we need to transform them to fractions
Recall that given a mixed number of the form
[tex]a\frac{b}{c}[/tex]we can transform it into a fraction by multiplying the whole number by the denominator and adding the result to the numerator while leaving the denominator fixed. In this case, that is
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex]So, applying this formula to both numbers, we get
[tex]3\frac{1}{4}=\frac{3\cdot4+1}{4}=\frac{13}{4}[/tex]and
[tex]5\frac{1}{2}=\frac{5\cdot2+1}{2}=\frac{11}{2}[/tex]so the area of the parallelogram would be
[tex]\frac{13}{4}\cdot\frac{11}{2}=\frac{143}{8}\approx18[/tex]so the area of the parallelogram is approximately 18 square yards
Write an inequality:Carlos was going to sell all of his stamp collection to buy a video game. After selling half of them he changed his mind. He then bought twelve more. How many did he start with if he now has at least 29?
Answers
Answer:
He started with at least 34 stamp collection
Explanation:
Let x represent Carlos' initial stamp collection.
From the question, we're told that he sold half of them, bought twelve more, and currently has at least 29, we can go ahead and set up an inequality as shown below;
[tex]\frac{x}{2}+12\ge29[/tex]We can go ahead and solve for x following the below steps;
Step 1: Subtract 12 from both sides of the equation;
[tex]\begin{gathered} \frac{x}{2}+12-12\ge29-12 \\ \frac{x}{2}\ge17 \end{gathered}[/tex]Step 2: Multiply both sides by 2;
[tex]\begin{gathered} \frac{x}{2}\times2\ge17\times2 \\ x\ge34 \end{gathered}[/tex]From the above, we can say that Carlos started with at least 34 stamp collection