Sammy's Chipmunk & Squirrel Observations
For a science project, Sammy observed a chipmunk and a squirrel stashing
acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The
squirrel hid 4 acorns in each of the holes it dug. They each hid the same number
of acorns, although the squirrel needed 4 fewer holes. How many acorns did the
chipmunk hide?

Answers

Answer 1

Answer:12 accorns

Step-by-step explanation:

Answer 2

If they each hid the same number of acorns, although the squirrel needed 4 fewer holes, the chipmunk hid 3 acorns in each hole

Let's assume the number of holes the chipmunk dug is 'c', and the number of acorns it hid in each hole is 'x'. Similarly, let's assume the number of holes the squirrel dug is 's', and the number of acorns it hid in each hole is 'y'.

According to the information provided, the chipmunk hid 3 acorns in each of the holes it dug, so x = 3. The squirrel hid 4 acorns in each of the holes it dug, so y = 4.

Both the chipmunk and squirrel hid the same number of acorns, so cx = sy.

Also, the squirrel needed 4 fewer holes, so s = c - 4.

Now, we can use the information to set up a system of equations:

cx = sy

c - 4 = s

Substitute the value of s from the second equation into the first equation:

c(c - 4) = 3(c - 4)

Expand the equation:

c² - 4c = 3c - 12

Now, bring all terms to one side of the equation:

c² - 4c - 3c + 12 = 0

Combine like terms:

c² - 7c + 12 = 0

Now, factor the quadratic equation:

(c - 3)(c - 4) = 0

Now, set each factor to zero and solve for 'c':

c - 3 = 0 => c = 3

c - 4 = 0 => c = 4

Since the chipmunk hid 3 acorns in each hole, the correct answer is The chipmunk hid 3 acorns.

To learn more about equations click on,

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Related Questions

1038*472 please help

Answers

Answer:

443,226

Step-by-step explanation:

What is the missing number in the table

Answers

16
Because the pattern is *4
So 4*4 =16

The area of each square tile is square feet and the area of each triangular tile is square foot.

We will pour sand into each frame to a depth of foot.

image placeholder
ft
Complete the sentence with the amount of sand we will need for each tile.​

We will need

ft of sand for each square tile, and

ft of sand for each triangular tile.

Answers

Answer

hi

Step-by-step explanation:

ok

I need help with math

Answers

51+60= 111 Answers fast rights

Help help math math

Answers

Answer:

5/1

Step-by-step explanation:

the y is 5units and the x is 1unit

Answer:

7/4

Step-by-step explanation:

Use rise over run to solve

4-(-3)         7

-------- =      -

6-2            4

What is the percent decrease from 95 to 68 round to the nearest percent

Answers

The decrease is  (95-68) = 27 .

As a fraction, the decrease is  27/95  of the original amount.

To change any fraction to a decimal, do the division:

                            (27)  divided by  (95) = 0.2842...

To change any decimal to a percentage, move the

decimal point two places that ==> way:

                            0.2842...  =  28.42... %Answer:

Step-by-step explanation:

[tex]\qquad[/tex]☀️ At first we need to find out the difference between 95 and 68.

[tex]\qquad[/tex][tex] \sf \longrightarrow 68 -95 \\[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow -27[/tex]

[tex]\qquad[/tex]☀️ Now, divide the number by "the starting number.

[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{-27 }{97}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow -0.2842[/tex]

[tex]\qquad[/tex]☀️ And finally, we have to multiply the result by 100 to get it in terms of percent.

[tex]\qquad[/tex][tex] \sf \longrightarrow -0.2842 \times 100[/tex]

[tex]\qquad[/tex][tex] \red{\bf \longrightarrow -28.42℅}[/tex]

Hence, The answer will be -28.42℅

[tex]\qquad[/tex]_________________________

Solve for x.
8x - 5 = 6x + 8x + 10

Answers

Answer:x = -5/2Step-by-step explanation:8x - 5 = 6x + 8x + 10=> 8x - 14x = 5 + 10=> -6x = 15=> x = -15/6=> x = -5/2Conclusion:

Therefore, we found that x = -5/2.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

the answer is x=-5/2

Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.​

Answers

Answer:   [tex]\boldsymbol{-25+18\sqrt{2}}[/tex]

The expression is in the form [tex]a+b\sqrt{2}[/tex] where a = -25 and b = 18

==========================================================

Work Shown:

Let [tex]x = 3\sqrt{2}[/tex] and then square both sides

[tex]x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\[/tex]

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\[/tex]

[tex]\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}[/tex]

Therefore,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}[/tex]

-------------------------------------

Checking the answer:

Use a calculator to find that,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571[/tex]

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

Evaluate the expression 2-8 × 2-7=

Answers

Answer:

-21

Step-by-step explanation:

2-8 × 2-7 = 2-(8×2)-7

= 2-16-7

=-14-7

=-21

Find the least common denominator for these fractions. Enter your answer in
the space provided.

Answers

Answer:

10

Step-by-step explanation:

"Least" means smallest.

"Common" means same.

"Denominator " means the bottom number in a fraction.

Something/2 can be changed to something/10

AND something/5 can also be changed to

something/10

1/2 >>>> 5/10

3/5 >>>> 6/10

10 is the least common denominator.

If sinA=1/7, sinB=1/3.
Prove: cos2A=sin4A​

Answers

Answer:

Question!! What is the relationship between A and B?

Step-by-step explanation:

Can someone help me? Will mark brainiest :)

Answers

the anser is 2 cuz i sad so, and i was droped don te stars as a lil kid ÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆ

HELP ME!! (I WILL GIVE BRAINLIEST!)

Answers

Answer:

|-5| absolute be always + so 5

Answer:

[tex]5[/tex]

Step-by-step explanation:

Step 1:  Determine what absolute value does

Taking the absolute value of a number just returns how far a specific value is from 0.  So in this case we see a number -9 and although it's negative it's still 9 away from 0 therefore that would be the absolute value.

We are missing the absolute value of -5 or 5 so we know that taking the absolute value would just give us the distance from 0.  In this case that would just be 5.

Answer: [tex]5[/tex]

-6x+6y=9 (1/2,2) please helppppp

Answers

Answer:

A. Solution

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinate Planes

Coordinates (x, y)

Step-by-step explanation:

*Note:

A coordinate is a solution if both the left side and right side of the equation is equal.

Step 1: Define

Identify.

-6x + 6y = 9

(1/2, 2)

Step 2: Verify

Substitute in variables [Equation]:                                                                   -6(1/2) + 6(2) = 9[Order of Operations] Evaluate:                                                                      9 = 9

Since 9 does indeed equal 9, the coordinate (1/2, 2) is a solution.

9. The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm2,
find its length and the width.

Answers

Answer:

  length: 13 cm

  width: 5 cm

Step-by-step explanation:

You may be aware that 65 = 5×13. We note that 13 is 3 more than twice 5, so these are the dimensions of the rectangle:

  5 cm wide; 13 cm long

__

If you want so solve this algebraically, you can let w represent the width. Then the length is 2w+3 and the area is ...

  A = LW

  65 = (2w+3)(w)

In standard form, this equation is ...

  2w^2 +3w -65 = 0

To factor this, you look for factors of 2×(-65) = -130 that have a sum of 3. Those would be ...

  -130 = (-10)(13)

Then the factored equation is ...

  2w^2 +13w -10w -65 = 0

  w(2w+13) -5(2w+13) = 0

  (w -5)(2w +13) = 0   ⇒   w = 5, -13/2

The positive solution makes sense in this problem, so ...

  width = 5 cm

  length = 2(5) +3 = 13 cm


give a pair of alternate interior angles, a pair of corresponding angles and a pair of alternate exterior angles.

Answers

alternate interior: 6&3
corresponding: 5&7
alternate exterior: 8&1

HELPPP!! DUE NOWWWW!

Lucy recently joined a fitness club, she had to pay an initial fee to join. Lucy will also pay an extra fee per class she takes there. The equation below represents the relationship.


f(x)=20+3x


Identify the false statement


A. Lucy paid $3 per class.

B. f(x) represents the total amount Lucy paid.

C. x represents the cost of classes.

D. The initial fee was $20

Answers

Answer: C

Step-by-step explanation: x represents the number of classes, not the cost of classes.

3. Find the area of the trapezoid.
8 ft
4V3
10 ft

Answers

Answer:

[tex]32\sqrt3[/tex]

Step-by-step explanation:

We need first to find the measure of the red horizontal line, call it x. The triangle i filled is a right triangle, so we can apply pythagoras theorem,

[tex]8^2 = x^2+(4\sqrt3)^2 \rightarrow 64=x^2+(16\times3) \\x^2=64-48 \rightarrow x^2=16 \rightarrow x=4[/tex]

(we are talking lengths of segment so we take only the positive root!)

At this point we can find the length of the smaller base of the trapezoid (which is [tex]10-4=6[/tex]) and apply the formula, or split the figure in a rectangle of sides 6 and [tex]4\sqrt3[/tex] and a triangle of sides [tex]4\sqrt3[/tex] and 4.

With the trapezoid formula

[tex]A=\frac12(B+b)h = \frac12(10+6)4\sqrt3 = 32\sqrt3[/tex]

With the sum of figures:

[tex]A= bh+\frac12 xh=6\times4\sqrt3 +\frac12\times4\times4\sqrt3=24\sqrt3+8\sqrt3=32\sqrt3[/tex]

6. Rachael is married with 2 dependents. Her salary as a dental hygienist is $47,650 paid
in 26 pay periods. Find the state tax withheld per pay period.

Answers

Answer:1.2389 million US$

Step-by-step explanation:

solve: s=4 + square rooted s+5

Answers

S=2.6 Because the square root of four hours to and it is 2.6

Manny borrowed $800 at 10% annual interest. How much interest did he owe in one year?

Answers

Answer:

80

Step-by-step explanation:

Giving 100 points for this and Brainliest!!

Well I ask this question for 100 points: I don't know how much it will give you

Please give me an explanation, no link please:

Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?

Answers

Answer: Sarah found 10 shark teeth(3 + 7 = 10).

John found 5 shark teeth(10/2 = 5).

The total money they earned was $5 x 15 = $75.

Explanation;

Given that:

$5 per shark tooth15 total collected shark teeth

5 x 15 = 75, therefore the total money Sarah and John earned was $75.

The few sentences to end Sarah's story are: Sarah found 10 shark teeth for $50. John found 5 shark teeth for $25. They got $75 from their neighbor in total.

Answer:

Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

Part 1: Writing Expressions

Q1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.

25(10j + 18 + 5j)

Step-by-step explanation:

1/8+1/4=? do you know what it could be!?

Answers

Answer:0.375

Step-by-step explanation:

1/8 + 1/4 = 3/ 8=0.375

Jordan made this design from three pieces of square shaped cloth. What is the total area of design Jordan made? EXPLAIN how u found your answer

Answers

Applying the area of a square, the total area of the design is: 116 cm²

Area of Square

A square has equal side lengths, s, this, the area of a square is given as: A = s².

The three pieces of square shaped cloth that Jordan made the design from is shown in the image attached below.

To find the total area of the design, find the area of each square shaped cloth and add all together.

Thus, applying the area of a square, the total area would be:

Total Area = 4² + 6² + 8²

Total Area = 116 cm²

Learn more about area of square on:

https://brainly.com/question/16758129

According to the telegram which of the following description of the data are true

Answers

Answer:ITS THE SECOND ONE

Step-by-step

Solve. 6 Everyone at a park was either hiking or riding a bike. There were 24 more hikers than bike riders. If there were a total of 100 people at the park, how many were hiking?​

Answers

b r = 178 + h;

b r + h = 676;

then, 178 + 2h = 676 => h = 498/2 = 249 => b r = 178 + 249 = 427

Answer:

676

Step-by-step explanation:

h=b+178=427

b=b=249

-------------

(b+178)+b=676

2b+178=676

2b=498

b=249

-------------

249+427=676

Kaneppeleqw and 2 more u

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answer:

[tex]I(-2,0) \to\\ I \ ' \ (-0.5,0)\\\\J(3,2) \to\\ J \ ' \ (0.75,0.5)\\\\K(1,-1) \to\\ K \ ' \ (0.25,-0.25)\\\\[/tex]

==================================================

Explanation:

For each point, multiply each x,y coordinate by 0.25 (the scale factor) to dilate the preimage to the image. This will shrink the image because the positive scale factor is less than 1.

So for instance, point J(3,2) will have this scratch work

3*(0.25) = 0.752*(0.25) = 0.5

meaning J(3,2) moves to J ' (0.75, 0.5)

----------

Side notes:

0.25 = 1/40.5 = 2/4 = 1/20.75 = 3/4this trick only works if the center of dilation is the origin

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.4 times every eight hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open.
(a) Explain why the Poisson probability distribution would be a good choice for the random variable r.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

What is ? (Round your answer to three decimal places.)


(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Round your answer to four decimal places.)


(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Round your answer to four decimal places.)


(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Round your answer to four decimal places.)

Answers

Using the Poisson distribution, it is found that:

a) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.b) 0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.c) 0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.d) 0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.

Item a:

In this problem, we are given the mean during an interval, which is a common event(1.4 every 8 hours), and intervals can be assumed to be independent, hence, the correct option is:

Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

Item b:

Mean of 1.4 every 8 hours, hence, every 11 hours, the mean is:

[tex]\mu = 11 \times \frac{1.4}{8} = 1.925[/tex]

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1459 = 0.8541[/tex]

0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.

Item c:

The probability is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

[tex]P(X = 1) = \frac{e^{-1.925}(1.925)^{1}}{(1)!} = 0.2808[/tex]

[tex]P(X = 2) = \frac{e^{-1.925}(1.925)^{2}}{(2)!} = 0.2703[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1459 + 0.2808 + 0.2703 = 0.697[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.697 = 0.303[/tex]

0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.

Item d:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.

To learn more about the Poisson distribution, you can take a look at https://brainly.com/question/13971530

In the New York marathon there were 45 360 runners. 7 /10 of the runners were women. How many of the runners were men? ​

Answers

Answer:

13,608

Step-by-step explanation:

If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.

Hope this helps! Pls give brainliest! Also, plz sub to kgirl633 on yt.

Karma took a 50 question math test, but only 40 questions were correct. What was the percentage of correct answers?

Answers

Answer:

85 percent

Step-by-step explanation:

Other Questions
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