2. PB and J Array Ken has made a selection of square jam sandwiches for party, which he arranges in a single layer on the table in perfect rectangle. Sarah has brought along the same number of square peanut butter sandwiches, which she puts out, also as a single layer, to form a border vA (one sandwich wide) around Ken's Given that all of the sandwiches are the same size and they are all used, how many sandwiches could each person possibly have made?
Answers
Each person must have made 24 sandwiches.
Let's assume Ken arranged his sandwiches in a rectangular shape with length 'L' and width 'W'. Now Sarah arranged her sandwiches to form a border around Ken's rectangle. The solution diagram is attached below.
Ken needs as much sandwiches as area of rectangle i.e. number of Ken's sandwiches would be = LW.
It is clear that Sarah needs as much sandwiches as perimeter of rectangle and extra four sandwiches to put on corners. It means number of Sarah's sandwiches would be = 2·(L+W) + 4.
Given that all of the sandwiches are the same size and they are all used.
Ken and Sarah bought same number of sandwiches. So we need to solve the following equation :-
Number of Ken's sandwiches = Number of Sarah's sandwiches
LW = 2·(L+W) + 4
Using trial and error approach, we get 6 x 4 = 2 x (6 + 4) + 4.
So number of Ken's sandwiches would be LW = 6 x 4 = 24 sandwiches.
Hence, final answer is "Each person could have 24 sandwiches".
Related Questions
Delia spent 45 minutes working on her book report. She finished the report at 6:10 p.m. at what time did Delia start working on her report
Answers
just act like the time is 6:00 then minus 45 and add 10 to your answer.
Bob's tire outlet sold a record of tires last month one sales ma sold 165 tires which was 60 percent of the record what was the record number
Answers
165/x=60/100
165 times 100=16500
16500/60=275
x=275
Answer:
The record number was 275 tires.
165/x=60/100
165 times 100=16500
16500/60=275
x=275
Step-by-step explanation:
Kasimir rode his bike 34,478 centimeters. He converts the distance to kilometers. His work is shown below.
A.Kasimir should have divided by 10,000.
B.Kasimir should have multiplied by 100.
C.Kasimir should have divided by 100,000.
D.Kasimir should have multiplied by 0.001.
Answers
Answer:
c) Kasimir should have divided by 100,000.
Step-by-step explanation:
Given that Kasimir rode his bike 34,478 centimeters.
We have the table
10 mm=1 cm
10 cm =1dm
10dm = 1 m
...
Hence we have 100 cm = 1 m
100x1000 cm = 1 km
1 km = 34478/100000 = 0.34478
Hence C) is right
Kasimir should have divided by 100,000.
Madame pompadour recently purchased velvet-lined doggy basket and a Diamond studded flea collar as a birthday gift for her beloved pet poodle. If the two items cost $3,215.90 and $ 5,850.25 Respectively what was the total bill
Answers
a dog pen measures 4 meters wide and has an area of 20 square meters. what is the perimeter of the pen in meters
Answers
So, we use this formula when finding the area of a rectangle:
A = l × w
The formula for perimeter:
P = 2l + 2w
We have the width but we still need the length to find the perimeter. You see, we multiplied the length by the width to get the AREA, but because we want to find the opposite now, we must use the opposite operation as well.
What's the opposite of multiplication?
Division!
Formula for length:
L = A ÷ w
Substitute:
L = 20 ÷ 5
L = 4 meters
Now that we know what the length and the width of the dog pen is, finding the perimeter will be a piece of cake!
Formula:
P = 2l + 2w
Substitute:
P = 2(4) + 2(4)
P = 16 meters
A N S W E R:
The perimeter of the dog pen is 16 meters.
The movie theater received a shipment of candy boxes in a carton that has a volume of about 64,000 cubic inches. Each candy box is 6 inches by 5 inches by 1/2 inch. The carton is completely full. About how many candy boxes are in the carton?
About 2,000
About 10,000
About 1,000
About 4,000
Answers
Volume of a candy box= 6 inx 5 inx 1/2
Volume of a candy box=15 inches³
Then, you have that the total candy boxes in the carton is:
x=640000 inches³/15 inches³
x=4267 candy boxes
About how many candy boxes are in the carton? There are 4267 candy boxes
[tex]V=(6)(5)( \frac{1}{2} )[/tex]
[tex]V=15[/tex]
Now that we know the volume of each candy box, we can divide the total volume 64000 [tex]in^{3} [/tex] by the volume of each candy box to find how many of them are in the carton:
[tex] \frac{64000}{15} =4266.67[/tex]
We can conclude that there are about 4000 candy boxes in the carton.
Jesse has a storage container in the shape of a right rectangular prism. The volume of the container is 43.875 cubic meters, the length is 5 meters and the width is 3.9 meters.
What is the height of Jesse's storage container?
I NEED HELP!!!!!!!!!!!!!!!!!!!!!!! :(
Answers
Answer:
2.25 meters
Step-by-step explanation:
all you have to do is divide the volume of the container (43.875) by 5 (length) and 3.9 (width) because the formula for the volume of a rectangular prism is V=lwh. So the answer/height of the storage container is 2.25 meters.
In 7 minutes, Jo swims 12 laps. If she maintains the same pace, how long will it take Jo to swim 30 laps? SHOW ALL WORK. Answer the question using a complete sentence PLEASE...
Answers
First, we have to figure out how many 12 laps are in 30 laps.
30/12 = 2.5
Since this is a proportion, we have to apply the same 2.5 to 7 minutes.
7 * 2.5 = 17.5 minutes.
It would take Jo 17.5 minutes to complete 30 laps.
Hope this helps!
Factor 64 – x15. (4 – x3)(16 + 4x3 + x3) (4 – x3)(16 + 4x3 + x6) (4 – x5)(16 + 4x5 + x5) (4 – x5)(16 + 4x5 + x10)
Answers
I hope this helps!
Answer:
Option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
Step-by-step explanation:
We are given the following in the question.
[tex]64-x^{15}[/tex]
We have to factorize the given expression.
Using the algebraic identity:
[tex]a^3 - b^3 = (a-b)(a^2+b^2+ab) = (a-b)^3 +3ab(a-b)[/tex]
[tex]64-x^{15}\\\\(4)^3 - (x^5)^3\\\\(4 - x^5)(4^2 + (x^5)^2 + 4x^5)\\\\(4-x^5)(16+x^{10}+4x^5)[/tex]
Hence, the factors of given expression is given by option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
2 and 1/3 + 1.5x = 12.3. What is x?
Answers
Here is what I got (Red represents my work, blue represents to follow which steps and highlighter represents what the answer is):
The Pythagorean theorem is used to prove that a triangle is a(n) triangle.
Answers
The Pythagorean theorem is used to prove that a triangle is a right triangle.
We also have Pythagorean triangle. This is known as primitive right triangle.
The used of the said theorem is to prove that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs. One of the studies said that the theorem is talking about the area of the squares that are built on each side of the right triangle.
Answer:
Right
Step-by-step explanation:
Use the net to compute the surface area of the three-dimensional figure. A) 210 units2 B) 225 units2 C) 240 units2 D) 280 units2
Answers
The surface area of the given three-dimensional figure is 210 square units.
Option A will be the correct answer.
Surface Area of CuboidA cuboid is a three-dimensional figure having length, width and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.
For the given cuboid, length l = 8 , width w = 5 and height h = 5.
Area of Cuboid = 2 lw + 2 lh + 2 wh
[tex]A = 2\times l\times w + 2 \times l\times h + 2\times w\times h[/tex]
Substituting the values in the above formula, the area will be,
[tex]A = 2 \times 8 \times 5 + 2 \times 8 \times 5 + 2\times 5\times 5[/tex]
[tex]A = 210 \;\rm {units}^2[/tex]
Hence, the surface area of the cuboid is 210 square units.
To know more about the surface area of cuboids, follow the link given below.
https://brainly.com/question/9740924.
Please Answer ASAP!
Seventy-five bottles of water are randomly tested from the large inventory in a warehouse. Which term refers to the large inventory of water bottles in the warehouse?
A. outlier
B. parameter
C. population
D. sample
Answers
Is the system of equations is consistent, consistent and coincident, or inconsistent? y=4x−4 y=−4x+4 Select the correct answer from the drop-down menu.
Answers
If a system has exactly one or infinite number of solutions then it will be a consistent system.
So, we can solve the given system of equation to get the answer.
y=4x−4 ................(1)
y=−4x+4...............(2)
After equating both the equations we will get,
4x-4= -4x+4
4x-4+4x=4 (Adding 4x to each sides).
8x-4=4
8x=4+4 (Adding 4 to each sides).
8x=8
8x/8=8/8 ( Dividing each sides by 8).
x=1
Now pluging x=1 in equation (1). So,
y=4x−4
=4(1)-4
=4-4
=0
Hence the solution of the given system is (1, 0) which also means that the two equations is intersecting at a point(1,0).
So, the given system is consistent and coincident.
Answer:
The answer is " Consistent And Independent"
Why? :
When 2 Lines intersect at one point it means it Consistent and Independent
and When the Lines are the same exact thing its Consistent and Dependent
But, when 2 lines don't intersect at all its inconsistent. :)
I also Took The 5.11 Unit Test :)
*PLEASE HELP!!*
The population of a country is decreasing, and its population (in millions) over six years is shown in the table. Find an exponential regression curve to model this situation.
A.) y = 54.3(.918^×)
B.) y = 67.2(.887^×)
C.) y = 72.8(.842^×)
D.) y = 83.9(.903^×)
Answers
Ellen is drawing two polygons one of the polygons has 3 more angles than the other what shape could she be drawing
Answers
Answer:
Step-by-step explanation:
The attachment shows different types of polygons.
Now depending on these we have following five possibilities:
Case 1: Triangle and hexagon
If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.
Case 2: Quadrilateral and heptagon
If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.
Case 3: Pentagon and Octagon
If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.
Case 4: Hexagon and Nonagon
If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.
Case 5: Heptagon and Decagon
If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.
Depend on the possibilities, which figure Ellen is drawing.
What is polygon?A closed, two-dimensional form with straight line segments is called a polygon. It does not have three dimensions. A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. Depending on a polygon's number of sides.
Given Ellen is drawing two polygons one of the polygons has 3 more angles than the other,
Now, based on these, there are the five options listed below:
Case 1: Hexagon and triangle
If the first polygon is a triangle with three angles, the second polygon will be a hexagon with six angles.
Case 2: Heptagon and quadrilateral
If the first polygon has a quadrilateral shape and four angles, the second polygon will have four plus three more angles, making it a heptagon.
Pentagon and Octagon in Case 3
If the first polygon has a pentagon shape with five angles, the second will have an octagon shape with five plus three equals eight angles.
Hexagon and Nonagon in Case 4
If the first polygon has a hexagon shape and 6 angles, the second will have 6 + 3 = 9 angles and be a nonagon.
Heptagon and Decagon in Case 5
if the initial polygon is a hexagon, then The first polygon has 7 angles, the second has 7+3=10 angles, and the third is a decagon.
Hence the shape of polygon depend on these possibilities.
Learn more about polygon;
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Gabriel wants to solve the equation 5/8 m=25. What step should he do to get m by itself on one side of the equation?
Answers
5/8 m = 25
8(5/8 m) = 8(25)
5m = 200
He should then divide both sides by 5, to get rid of the coefficient
5m/5 = 200/5
m = 40
So m = 40 by these steps
Final answer:
To solve the equation 5/8 m = 25, Gabriel needs to multiply both sides of the equation by the reciprocal of 5/8, which is 8/5, to isolate m on one side. The result after simplification is m = 40.
Explanation:
To solve the equation 5/8 m = 25, Gabriel needs to isolate the variable m on one side of the equation. He should start by multiplying both sides of the equation by the reciprocal of the fraction that is multiplied by m, which is 8/5. Here's the step-by-step process:
Multiply both sides of the equation by 8/5 to cancel out the 5/8 on the left side:
(8/5) × (5/8) m = (8/5) × 25
Simplify the left side by canceling out the common factors in the fraction:
1 m = (8/5) × 25
Next, multiply the number 25 by 8/5 to find the value of m:
m = 25 × (8/5) = 40
Thus, the solution to the equation is m = 40.
PLEASE HELP BRAINLIEST REWARDED
Jamal drew the function below. Which explains whether or not his function is linear?
A. It is linear because it has a constant rate of change.
B. It is linear because it does not have a constant rate of change.
C. It is not linear because it has a constant rate of change.
D. It is not linear because it does not have a constant rate of change.
Answers
Hope I helped.Have a wonderful day.
Answer:
A. It is linear because it has a constant rate of change.
Step-by-step explanation:
A straight line graph is possible between two variables x and y only if there is a constant rate of change
y = mx+b is the equation of a straight line in general and here we find rate of change of y with respect to x is constant m which does not depend on x or y.
In other words, throughout the domain a straight line has constant slope.
Here we find that the graph given is a straight line.
Hence option A is suitable answer
A. It is linear because it has a constant rate of change.
The equation of the quadratic function represented by the graph y=a(x-3)-1 what is the value of a
Answers
Let a=2, if you like.
Use the Distributive Property to multiply. 3(2t – 8)
Answers
Answer 6t-24
Simplify this power raised to a power: (54)4
Answers
The value of [tex]$\left(5^4\right)^4$[/tex] simplified to [tex]$5^{16}$[/tex], meaning x = 16.
To simplify [tex]$\left(5^4\right)^4$[/tex], we first expand it as [tex]$5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4$[/tex], using four factors of [tex]$5^4$[/tex].
Applying the product of powers rule, we add the exponents together: [tex]$5^{4+4+4+4}$[/tex]. This simplifies to [tex]$5^{16}$[/tex].
In essence, raising a power to another power involves multiplying the exponents.
In this case, we have four factors of [tex]$5^4$[/tex], which means we multiply 4 by 4, resulting in [tex]$5^{16}$[/tex].
So, the value of x in the simplified power [tex]$5^x$[/tex] is 16.
Complete Question:
Simplify this power raised to a power: [tex]$\left(5^4\right)^4$[/tex]
1. Expand using four factors of [tex]$5^4$[/tex] : [tex]5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4[/tex]
2. Apply the product of powers rule: [tex]5^{4+4+4+4}[/tex]
3. Simplify: [tex]5^x[/tex]
What is the value of x in the simplified power?
I have to find the area
Answers
So, if we use this information....
4.2*5.5*1/2=11.55
Area=11.55
5.5 · 4.2 equals 23.1. You don't need the 6.9.
You then need to do 23.1 ÷ 2 which is 11.55 m².
Hope this helps!
The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compare to this number?
Suppose that the height of the slide is 2 feet, when x = 20. What is the average rate of change over the entire slide?
Answers
We have:
R = ((80-10) / (0-15))
R = -4.666666667
We now calculate for the entire interval:
from x = 0 to x = 20:
R = ((80-2) / (0-20))
R = -3.9
Answer:
What is the average rate of change over the entire slide?
R = -3.9
The average rate of change from x = 0 to x = 15 is about -4.667. How does the average rate change from x = 0 to x = 20 compare to this number?
The percentage difference is:
(-3.9 / -4.666666667) * (100) = 83.57142857%
100-83.57142857 = 16.42857143%
The average rate of change over the entire slide is -0.05.
The average rate of change from x = 0 to x = 15 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 15.
The slope of the secant line is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (-2 - 15)/(15 - 0)
= -17/15
= -1.133
The average rate of change from x = 0 to x = 20 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 20.
The slope of the secant line is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (2 - 15)/(20 - 0)
= -13/20
= -0.65
The average rate of change from x = 0 to x = 20 is smaller than the average rate of change from x = 0 to x = 15.
This is because the slope of the secant line is getting closer to 0 as the interval gets larger.
If the height of the slide is 2 feet when x = 20, then the average rate of change over the entire slide is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (2 - 1)/(20 - 0)
= -1/20
= -0.05
The average rate of change over the entire slide is also negative, but it is much smaller than the average rate of change from x = 0 to x = 15.
This is because the slope of the secant line is getting closer to 0 as the interval gets larger.
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If the power required to lift a weight of 10 N in 3 seconds is 60 W, what is the distance the weight moves? A. 1m B. 6m C.18m D.36m
Answers
Power = [work done]/[time taken]
work done=power*time taken
power---------- > 60 W
time taken------ > 3 sec
then
work done=60*3=180 J
and we know
work done=Force*distance
distance=[work done]/[force]
work done=180 J
force=10 N
distance=180/10=18 m
the answer is the option C.18m
Jake purchased a box of 1000 candy guitar lollipops to sell in the bakery for20. 00 how much did you pay for each lollipop
Answers
Just divide 1000/20 to see how much you payed for each lollipop. The answer is 50!
Hope this helps!
5.65 times 3.4 estimate
Answers
3 * 6 = 18
now let's see how close our estimate is to the real answer
5.65 * 3.4 = 19.21
Our answer was pretty close to the real answer!
Hope I helped!
~ Zoe
studying for the act and I'm really bad at math, please help!
Answers
Multiply both sides of the ratio by 2. I'm doing this so that the "1/2" turns into "1"
So we go from this ratio
1/2 inch: 18 miles
to this ratio
1 inch: 36 miles
which means that every inch on paper represents 36 miles in real life
----------------------------------------------------------------
The question is now: if two towns are 2.5 inches apart on paper, then how far are they in real life? (note: 2.5 is the decimal form of 2 and a half)
To find out, multiply both sides by 2.5
1 inch: 36 miles
2.5*(1 inch): 2.5*(36 miles)
2.5 inches: 90 miles
--------------------------------------------------------------------------
Answer: The two towns are 90 miles apart in real life
Dora is purchasing a $162,000 home with a 30-year mortgage at 5.15%. What is her monthly principal and interest payment?
A. $829.23
B. $884.56
C. $807.81
D. $876.09
Answers
Answer:
B . $ 884.56
Step-by-step explanation:
Since, monthly payment formula of a loan,
[tex]P=\frac{PV(\frac{r}{12})}{1-(1+\frac{r}{12})^{-12t}}[/tex]
Where,
PV = principal value,
r = annual rate of interest,
t = number of years,
Here,
PV = $ 162,000,
r = 5.15% = 0.0515,
t = 30,
Hence, the monthly payment would be,
[tex]P=\frac{162000(\frac{0.0515}{12})}{1-(1+\frac{0.0515}{12})^{-360}}[/tex]
[tex]=\$ 884.562485827[/tex]
[tex]\approx \$ 884.56[/tex]
OPTION B is correct.
a triangle has a base of 15 in. and an area of 82.5 square inches. what is the height of the triangle? please explain how u found the answer out :)
Answers
.. A = (1/2)*b*h
.. 82.5 in^2 = (1/2)*(15 in)*h
.. 2*(85 in^2)/(15 in) = h
h = 11 in
You buy 8 packs of markers with 20 markers in each pack. You already had 10 markers. Which equation shows how to calculate the total number of markers, m, you have?
Answers
[tex](20 \times 8) + 10 = y[/tex]
I couldn't put m.
So y is m
Answer: [tex]m= 8(20)+10[/tex]
Step-by-step explanation:
Given : The number of markers in each of 8 pack = 20
Then, the number of markers in 8 packs = 8 x 20 = 8(20)
Also, You already had 10 markers.
Then, the total markers you have now = Number of markers in 8 packs+ 10
= 8(20)+10
If we denote the total number of markers be 'm'.
Then, the required equation will be :-
[tex]m= 8(20)+10[/tex]
Hence, the equation shows how to calculate the total number of markers, m, you have : [tex]m= 8(20)+10[/tex]