Pensils are sold in packages of 10 and erasers are sold in packages of 6. What is the least number of pensils and erasers you can buy so that there is one pencil for each eraser with none left over.

Answers

Answer 1

To understand the problem consider the following cases.

i)

If we buy 1 packet of pencils, and 2 packet of erasers,

we have 1*10=10 pencils and 2*6=12 erasers.

ii)

If we buy 3 packet of pencils, and 4 packet of erasers,

we have 3*10=30 pencils and 4*6=24 erasers.

So let a and b be the correct number of packets of pencils and erasers respectively.

That is the least numbers a and b, such that 10a=6b.

10a=6b

divide both sides by 10:

[tex]a= \frac{6b}{10}= \frac{3b}{5}[/tex]

divide both sides by b:

[tex] \frac{a}{b} = \frac{3}{5} [/tex]

the ratio a:b cannot be simplified any further. This means that the smallest (natural) numbers a and b such that [tex] \frac{a}{b} = \frac{3}{5} [/tex] are a=3 and b=5

Answer:

3 packages of pencils, 5 packages of erasers.

Related Questions

A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price

Answers

Final answer:

The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.

Explanation:

To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:

$15 × 0.35 = $5.25

This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:

$15 + $5.25 = $20.25

Therefore, the selling price of the product would be $20.25.

Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.

Answers

The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour

The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.

$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.

for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value

Answers

Assuming the function is

[tex]y=-2+5\sin\left(\dfrac\pi{12}(x-2)\right)[/tex]

recall that [tex]-1\le\sin x\le1[/tex], which means

[tex]-1\le\sin\left(\dfrac\pi{12}(x-2)\right)\le1[/tex]
[tex]\implies-5\le5\sin\left(\dfrac\pi{12}(x-2)\right)\le5[/tex]
[tex]\implies-7\le-2+5\sin\left(\dfrac\pi{12}(x-2)\right)\le3[/tex]

and so the minimum value is -7.

Answer:

-7

Step-by-step explanation:

We are given that a function

[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]

We have to find the minimum value of y.

We know that range of sin x is [-1,1].

[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]

[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]

[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]

[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]

[tex]-7\leq y\leq 3[/tex]

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7

Explain how you can use place value patterns to describe how 50 and 5000 compare

Answers

The place value pattern is a system of patterns of tens in which every place value is ten times the value on its right. The place value pattern system is used to write numbers that are 10 times as much as or 1/10 of any given number.
The place values in the pattern are: ones, tens (10*ones), hundreds (10*tens), thousands (10*hundreds),...
So, 50 = 5 tens
5000= 5 thousands, 0 hundreds, 0 tens, 0 ones

So, 5000 > 50

A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?

Answers

recall your d = rt, distance = rate * time

the rate going south is 13, the rate going east is 10

it took a total amount of 6hours and 72miles for the whole travel

so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles

so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours

thus [tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ South&d&13&t\\ East&72-d&10&6-t \end{array} \\\\\\ \begin{cases} \boxed{d}=13t\\ 72-d=10(6-t)\\ ----------\\ 72-\boxed{13t}=10(6-t) \end{cases}[/tex]

solve for "t"

so, it travelled East for 6-t hours

Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?

it's ((cos theta) * (cot theta))/(1-sin theta) - 1 = csc theta

Answers

[tex]\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{cos(\theta )cot(\theta )}{1-sin(\theta )}-1=csc(\theta )\\\\ -------------------------------\\\\ \cfrac{cos(\theta )\cdot \frac{cos(\theta )}{sin(\theta )}}{1-sin(\theta )}-1\implies \cfrac{\frac{cos^2(\theta )}{sin(\theta )}}{\frac{1-sin(\theta )}{1}}-1\implies \cfrac{cos^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{1-sin(\theta )}-1 \\\\\\ \cfrac{cos^2(\theta )}{sin(\theta )[1-sin(\theta )]}-1\implies \cfrac{cos^2(\theta )-1[sin(\theta )[1-sin(\theta )]]}{sin(\theta )[1-sin(\theta )]}[/tex]

[tex]\bf \cfrac{cos^2(\theta )-1[sin(\theta )-sin^2(\theta )]}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{cos^2(\theta )-sin(\theta )+sin^2(\theta )}{sin(\theta )[1-sin(\theta )]} \\\\\\ \cfrac{cos^2(\theta )+sin^2(\theta )-sin(\theta )}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{\underline{1-sin(\theta )}}{sin(\theta )\underline{[1-sin(\theta )]}} \\\\\\ \cfrac{1}{sin(\theta )}\implies csc(\theta )[/tex]

What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?

Answers

The formula of the future value of annuity ordinary is
Fv=pmt [(1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT monthly payment 35
R interest rate 0.07
K compounded monthly 12 because the payment is monthly
N time 30 years

Fv=35×(((1+0.07÷12)^(12×30)
−1)÷(0.07÷12))
=42,698.98

what is 475% of 9.2?

Answers

To find this, multiply 9.2 by the decimal form of the percent (4.75). The answer is 43.7

475% of 9.2 is =43.7

2/3 of a number is 32, what is the number?

Answers

2/3×a=32
a=32×3/2
a=96/2
a=48
The number is 48

2/3n = 32
Integers:- 3/2•2/3 = 32/1 = 3/2 = 96/2 = 48

The histogram shows the duration, in minutes, of movies in theaters.

What relationship between the median and mean is shown by the histogram?

A) The mean is less than the median.

B) The median is less than the mean.

C) The mean is equal to the median.

D) The median and mean cannot be compared from a histogram.

Answers

A histogram is a type of bar graph that presents the frequency of your data. In this problem, the histogram shows the frequency of movies (y-axis) with respect to the minutes of their duration (x-axis). Example, there are 2 movies that have a duration of 84-91 minutes, 4 movies having a duration of 91-98 minutes, and so on and so forth.

The mean of these data is (2+4+5+4+3+3+2+2)/8 = 3.125
The median is the middle data when the frequency is arranged from least to greatest. Thus, the median in the data set 2, 2, 2, 3, 3, 4, 4, 5 is 3. Therefore, the mean is greater than the median.

The answer is: the median is less than the mean

mean is equal to median.

An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees

Answers

0.3(8.59) = 2.577 rounds to 2.58 acres

How many solutions to 15x+11=8x

Answers

To get the number of solutions in the equation given we shall be required to solve the equation;
15x+11=8x
collecting like terms we get:
11=8x-15x
11=-7x dividing both sides by -7 we get:
x=-7/11
therefore we conclude that the number of solutions is one

Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero

Answers

Since 10 out of 14 marbles are green, the probability of selecting a green marble is 10/14=0.714.

Similarly, the probability of selecting a red marble would be 4/14.

Answer: 0.714

Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}

Answers

Let's do away first of the coding texts. The given formula is 1/12 + 5/9. If you want to automatically know the answer, then all you have to do is input this in a calculator and you would immediately get an answer of 23/36. But that would be too easy.

To solve this manually, you must find first the greatest common factor of the denominators. To do this, simply multiply 12×9 = 108. Now, you know that the final answer would have a denominator of 108.

1 5 [(108/12)*1] + [(108/9)*5]
--- + --- = -----------------------------------
12 9 108

Now for the numerator, you divide the denominator, 108, to each of the addends, 12 and 9. Then, multiply it with their respective numerators. The answer would then be 69/108. Both numerator and denominator are multiples of 3, so you can simplify them further by diving each with 3. The final answer is 23/36.

If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?

Answers

In this question, the prices are Increased at a monthly rate of 2.3%. Since you are asked how much the percentage in a year and there is 12 month in a year, then you need to do the calculation 12 times.

The calculation would be (100%+2.3%)^12= 131.37344984%

That would be about 31.37% a year.

Multiply and Dividing Rational Numbers

8/9 ÷ 2/3

7/8 × 1/4

3/4×1/6

Answers

essentially is just

[tex]\bf \cfrac{8}{9}\div \cfrac{2}{3}\implies \cfrac{8}{9}\cdot \cfrac{3}{2}\implies \cfrac{8\cdot 3}{9\cdot 2}\implies \cfrac{24}{18}\implies \cfrac{4}{3} \\\\\\ \cfrac{7}{8}\cdot \cfrac{1}{4}\implies \cfrac{7\cdot 1}{8\cdot 4}\implies \cfrac{7}{32} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3\cdot 1}{4\cdot 6}\implies \cfrac{3}{24}\implies \cfrac{1}{8}[/tex]

At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?

Answers

The acceptable weight is within the range of [4, 7]

So the answer will be the 3rd graph

Answer: Third graph represents the acceptable weights for the frozen yogurt options.

Step-by-step explanation:

Since we have given that

Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4

After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.

So, it means the weight should be lie between 4 ounces and 7 ounces.

So, it can be written as [4,7].

4≤ x ≤7, here, x is the weight of frozen yogurt.

So, third graph represents the acceptable weights for the frozen yogurt options.

Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.

A. 30

B. 40

C.60

D. 80

Answers

Noel : 90 minutes a day for 6 days....90 * 6 = 540 minutes
Tyra : 60 minutes a day for 8 days....60 * 8 = 480 minutes

difference of : 540 - 480 = 60 <==

The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.

The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.

Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.

A home pregnancy test is not always accurate. suppose the probability that the test indicates that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates that a woman is not pregnant when she really is, is 0.03. assume that the probability that a woman who takes the test is actually pregnant is 0.7. what is the probability that a woman is pregnant if the test yields a not pregnant result?

Answers

Set Events:
T=tests positive~T=tests negativeP=subject is pregnant~P=subject is not pregnant
We are givenP(T n ~P)=0.02P(~T n P)=0.03P(P)=0.7
recall by definition of conditional probabilityP(A|B)=P(A n B)/P(B)

Need to find P(P|~T)
First step: make a contingency diagram of probabilities (intersection, n)
P ~P sum
T 0.67 0.02 0.69=P(T)
~T 0.03 0.28 0.31=P(~T)
sum 0.70 0.30 1.00
=P(P) =P(~P)

therefore
P(P|~T)=P(P n ~T)/P(~T)=0.03/0.31 [ both read off the contingency table ]
=0.0968

Final answer:

The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.

Explanation:

The subject of this question is based on conditional probabilities. From the question we know that:

The probability of the test indicating a woman is pregnant when she's not (false positive) is 0.02 i.e., P(Positive|Not Pregnant) = 0.02 The probability of the test indicating a woman is not pregnant when she actually is (false negative) is 0.03 i.e., P(Negative|Pregnant) = 0.03 The probability that a woman who takes the test is actually pregnant is 0.7 i.e., P(Pregnant) = 0.7

From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:

P(A|B) = P(B|A) * P(A) / P(B)

So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).

Learn more about Conditional Probability here:

https://brainly.com/question/10567654

#SPJ12

answer this plz

14 students are surveyed about the clothes they are wearing.

8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.

How many students are wearing jeans, but not a t-shirt?

2

3

4

5

Answers

The Correct Answer is B: 3 . Hope This Helps!

Answer:

its

Step-by-step explanation:

Gabrielle's age is three times Mikhail's age. The sum of their ages is 44. What is Mikhail's age?

Answers

g=gabby's age
m=micsdjfsdf's age

g=3m

sum is add
g+m=44

subsitute 3m for g
3m+m=44
4m=44
divide by 4 both sides
m=11

mikhail is 11 year old

Mikhail is 11 yrs old because 11 times 3 is 33. 33 plus 11 is 44

Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?

Answers

x = average of next 5 quizzes

4 * 73 = first 4 quizzes

There will be a total of 4 +5 = 9 quizzes

Average of all quizzes = 88 = (4*73+5x)/9

9*88 = 9*(292 +5x)/9

792 = 292 + 5x

500 = 5x

X = 500/5 = 100

Next 5 quizzes need to average 100

Find the area of sector AOB. Express your answer in terms of pi and rounded to the nearest tenth.

Answers

Final answer:

To find the area of sector AOB, use the formula A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, the area is approximately 0.139 m², rounded to the nearest tenth.

Explanation:

To find the area of sector AOB, we need to use the formula for the area of a sector: A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, we get A ≈ (1.11/360) * π * (4.5)^2.

Using a calculator, we can calculate the value to be approximately 0.139 m². Rounding to the nearest tenth, the area of sector AOB is 0.1 m².

Learn more about Area of a sector here:

https://brainly.com/question/29055300

#SPJ12

The areas of the sectors of circles 5 and 6 to the nearest tenth are 197.8 cm² and 6.3 ft² respectively.

What are the areas of the sectors?

The area of the sector of a circle can be expressed as:

Area = ( θ/360º ) × πr²

Where θ is the sector angle in degrees, R is the radius of the circle, and π is constant pi.

For question5)

Angle θ = 70 degrees

Radius r = 18 cm

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 70/360º ) × π × 18²

Area = 63π cm²

Area = 197.8 cm²

For question 6)

Angle θ = 180 degrees

Diameter d = 4ft

Radius r = 4/2 = 2ft

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 180/360º ) × π × 2²

Area = 2π ft²

Area = 6.3 ft²

Therefore, the area of the sector is 6.3 ft².

Learn more about area of sector here: https://brainly.com/question/32139306

#SPJ3

Need help with this word problem

Answers

check the picture below.

notice, we get -10 and 8, well, it cannot be a negative value, since it's the unit of a dimension.

so, the width is (1/2)x and the height is x+2.

Find the area of the shaded region below. The units are in feet.
Use 3.14 for π. Round your answer to two decimal places.

Answers

check the picture below.

so.. simply, get the area of the two circles, with radius of 4, we did that, and get the area of the larger circle with radius of 8, we did that.

now... keep in mind that, the area of the larger circle, includes the area of the two smaller circles, if you subtract the area of the two smaller circles from the larger's one, you're in effect making a hole in the larger circle, and what's leftover, is the shaded region.

The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?

Answers

To find the midpoint of line segment AB, we find the total distance for both x and y coordinates and then divide each answer by 2.

A (12, 7)
B (12, -3)

Mid point ([tex] \frac{12+12}{2} [/tex], [tex] \frac{7+-3}{2} [/tex])
Mid point ([tex] \frac{24}{2} [/tex], [tex] \frac{4}{2} [/tex]}
Mid point (12, 2)

Of the books in a library, 1/3 came from Robbie's collection and 15 came from Marta's. Of the rest, 15 were Elena's 1/5 were Winfield's, and 5 were purchased from the bookstore. How many book are there in the library?

Answers

library amount: l
Robbie: r=(1/3)l
Martha: m=15
rest of books: l-r-m=e+w+b
Elena: e=15
Winfield: w=1/5(e+w+b)
bookstore: b=5

w=(e+w+b)/5
w=(15+5+w)/5
w=4+w/5
(4/5)w=4
w=5

l-r-m=e+w+b
l-(1/3)l-15=15+5+5
(2/3)l=25+15
(2/3)l=40
l=60=amount of books

The total number of books in the library are 75.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

What will be the equation for given scenario?

Let the total number of books in the library be x.

The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]

Collect the like terms,

[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]

On solving the equation for x we get x=75.

Therefore, the total number of books in the library are 75.

Learn more: https://brainly.com/question/8806877

#SPJ2

A turkey was cooked at 300 f in the oven for 5 hours. the internal temperature rose from 35 f to 150 f. what was the average rise in temperature per hour

Answers

What do you think the answer is? Tell me and I will help you some more! :)

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. find the probability that the first card is an ace and that the second card is an ace?

Answers

4 aces in a deck

52 cards

you have a 4/52 reduced to 1/13 probability of picking an ace.

without replacing it there would be 51 cards left and 3 aces

so second probability of picking an ace is 3/51 reduced to 1/17

the probability of doing both = 1/13 x 1/17 = 1/221

Answer:

conf

Step-by-step explanation:

find the solution x-4y=9 and x-y=-9

Answers

see picture for solution

Other Questions

What is dharma? A.an individuals moral and religious duties B.the rebirth of the soul in another bodily form C.union with Brahma D.the essential self The human body can survive a negative acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2 (approximately 25g). if you are in an automobile accident with an initial speed of 76 km/h (47 mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you if you are to survive the crash? . Which of the following is the correct format for an MLA in-text citation for an article with no known author? A. (Title page) B. ("Title" page) C. "Title" page D. ["Title" page] Conflict theorists point out that a declining standard of living in society is likely to result in ________ in the respective country. How does the example of hatena and the alga represent an emergent explanation of life? What ideas about government could early american leaders have learned from the iroquois confederation? EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.A.) 5 inches B.) 25 inchesC.) 8 inchesD.) 26 inches Federal regulations mandate preadmission screening and resident review (pasrr) for Factor completely 2x3 + 14x2 + 4x + 28. Which polynomial is a perfect square trinomial? (1 point) 49x2 28x + 16 4a2 20a + 25 25b2 20b 16 16x2 24x 9? Please, would somebody help me solve this math problem? I have no idea how to solve it. Explain why the mean and standard deviation are not appropriate for particle size distributions Where does mother abbess hide the family in sound of music? Which verb best completes this sentence? Esta noche, nos ___________________________ en un albergue juvenil. visitaremos viajaremos iremos alojaremos Under what circumstance are two non right triangles congruent HELP If f(x)=15x+3, then f^-1(x)=? Simplifying expressions with exponents (05.01 MC)The table and the graph each show a different relationship between the same two variables, x and y:A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn. How much more would the value of y be in the table than its value on the graph when x = 11? 100 165 395 440 Mi padre quiere que nosotros _____ (asistir) a la iglesia. asistimos asistemos asistamos Which search would help you find critical essays on Cervantes work in an electronic catalog?A.Subject: CervantesB.Title: Don QuixoteC.Author: Cervantes, Miguel deD.Title: Literary Criticism Steam Workshop Downloader