Answer: a) Each group has 5 members as its greatest possible.
b) There are 4 groups of sixth graders and 5 groups of seventh graders.
Step-by-step explanation:
Since we have given that
Number of sixth grader = 20
Number of seventh grader = 25
We need to find the greatest possible number of members in each group will contain:
For greatest possible number we will find "Highest common factor (H. C.F) of 20 and 25 = 5
a) Each group has 5 members as its greatest possible.
b) Number of groups of sixth graders would be
[tex]\dfrac{20}{5}=4[/tex]
Number of groups of seventh graders would be
[tex]\dfrac{25}{5}=5[/tex]
Hence, there are 4 groups of sixth graders and 5 groups of seventh graders.
What is the distance between S and T? If necessary, round to the nearest tenth.
the value of the 7 in 507,264 is 10 times the value of the 7 in which number?
Answer:
The value of the 7 in 507,264 is 10 times the value of the 7 in number 2
Step-by-step explanation:
Given Number : 507,264
To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .
Starting from the left ,
4 is in ones place
6 is in tens place
2 is in hundreds place
7 is in thousands place
0 is in ten thousands place
5 is in lakhs place
Here, 7 is in thousands place
7000 = 10 x 700
2 is in hundreds place
200 = 2 × 100
Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in number 2 .
Find the product of 4×7×25tell which strategy you used
Based on the graph of the line below, which describes the relationship between the value of the y-intercept and the value of the slope?
after taking 1/4 pound of flour from a canister to make muffins, maria has 7/8 of the flour left. If each batch of muffins requires 2/5 pound of flour, find the greatest number of batches of muffins that Maria can make using the remaining flour/
A car is traveling at a rate of 40 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
1 mile = 1.6 kilometers
multiply 40 mph by 1.6 = 64
car's rate = 64 kilometers per hour
multiply kilometers per hour by 4 = 256
car will travel 256 kilometers in 4 hours
Which graph represents the function y=2/3x-2
Answer:
Here you go! used a graphing calculator for accuracy.
Step-by-step explanation:
what is a decimal number which never ends, but whose digits after the decimal point come in a predictable pattern called? it starts with the letters re.
6.14 x 10 to the power of negative 9 in standard form
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272. What amount is deducted from her pay for Social Security taxes if the rate is 6.2%? What amount is deducted for Medicare, which is taxed at 1.45%?
Answer:
The deduction for social Security tax is $4976.86 and the deduction for Medicare tax is $1163.94 .
Step-by-step explanation:
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272.
What amount is deducted from her pay for Social Security taxes if the rate is 6.2%?
[tex]0.062\times80272=4976.86[/tex] dollars
What amount is deducted for Medicare, which is taxed at 1.45%?
[tex]0.0145\times80272=1163.94[/tex] dollars
the difference of twice a number and 3
Which statement proves that PQRS is a parallelogram? The slopes of SP and RQ are both –2 and SP = RQ = . The slopes of RS and QP are both 3 and SP = RQ = . The midpoint of RP is and the slope of RP is . The midpoint of SQ is and SQ = 5
Answer:
The correct option is 1. The figure PQRS is a parallelogram, if slope of SP and RQ are both –2 and SP = RQ.
Step-by-step explanation:
The opposite sides of a parallelogram are parallel are equal.
In the quadrilateral PQRS,
PQ and RS are opposite sides.
SP and RQ are opposite sides.
The slope of two parallel lines are same.
If the slopes of SP and RQ are both –2. It means SP and RQ are parallel. It is also given that
SP = RQ
Since one pair of opposite sides are equal and parallel, therefore the another set of opposite sides is also parallel and equal.
The opposite sides are prallel and equation, so the quadrilateral PQRS is a parallelogram.
Thus correct option is 1.
The statement that proves that quadrilateral PQRS is a parallelogram is: A. The slopes of SP and RQ are both –2 and SP║RQ.
Properties of the Sides of a Parallelogram
A parallelogram is a quadrilateral having two pairs of opposite sides that are equal and parallel to each other, and also, the slopes of opposite sides of a parallelogram are the same.
Therefore, the statement that proves that quadrilateral PQRS is a parallelogram is: A. The slopes of SP and RQ are both –2 and SP║RQ.
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Barbara D’Angelo’s bank granted her a single-payment loan of $1,000 for 100 days at 12% ordinary interest. What is the amount of ordinary interest owed?
what is the value of this expression when x = -1 and y = 2?
4x³y²
Every 3 days Marco fills up his car with gas. Every 8 days he washes his car. On what day will Marco fill his car with gas and wash it?
Write an equation for "eight less than a number is seventy-five". What is the number? n - 8 < 75; -67 n - 8 = 75; 67 n - 8 = 75; 83 n - 8 < 75; 67
n-8=75
n is the number
so number minus 8 equals 75
if 2 out of every 20 ducks were banded, What percent were not banded?
if 2 were banded that means 18 out of 20 were not banded
18 divided by 20 = 0.9
so 90% were not banded
if it takes Joan one and a half hours to watch a movie, how many films can he watch in ten and a half hours
A six-sided rectangular box is to hold 1/2 cubic meter; what shape should the box be to minimize surface area?
A circle is an object which has the lowest surface area to volume ratio. So in this case, the shape should be like that of a circle but we cannot have a circle here because we want to form a 6 sided box. So the next thing closer to circle is a square. Hence the shape should be a square:
Answer:
square
To minimize surface area for a given volume of 1/2 cubic meter, the box should be shaped as a cube with each side measuring approximately 0.7937 meters. This cube shape offers the smallest surface area for the given volume.
Explanation:To minimize the surface area of a six-sided rectangular box with a volume of 1/2 cubic meter, it is best to make the box in the shape of a cube. This shape has the smallest surface area for a given volume. To find the dimensions of the box, let's denote the side of the cube as 's'. We know that volume V of a cube is given by V = s³. So, if the volume is 1/2 cubic meter, we have:
s³ = 1/2
s = ∛(1/2) ≈ 0.7937 meters
Each side of the cube should be approximately 0.7937 meters to achieve the minimal surface area. The surface area SA of the cube can be calculated as:
SA = 6s²
SA = 6 × (0.7937)² ≈ 3.770 meters²
Thus, a cube with sides of about 0.7937 meters will have the minimal surface area for a volume of 1/2 cubic meter.
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after 9 months, the simple interest earned on an investment of $1200 is $72. find the interest rate.
How to determine if the function has x-axis sym, y-axis sym, and origin sym
y^2 -xy =2
To check for symmetry on the x axis, replace y with –y
-y^2 –x(-y) =2
Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis
Now do the same for y axis by replacing x with –x
Again using product rule the equations are not identical, so it is not symmetric about the y axis
To check the origin,
Replace both x & y with –x & -y
Again using product rule, the equations are not identical so it is not symmetric about the origin
To check for symmetry, replace x with -x and y with -y in the equation. Upon doing that for y^2 -xy =2, we find it lacks x-axis, y-axis, and origin symmetry.
Explanation:To determine whether a function has x-axis symmetry, y-axis symmetry, or origin symmetry, we have to replace x with -x and y with -y and see whether we get the same function.
X-axis symmetry: Replace y with -y. The equation becomes (-y)^2-(-y)x=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no x-axis symmetry.Y-axis symmetry: Replace x with -x. The equation becomes y^2-(-x)y=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no y-axis symmetry.Origin symmetry: Replace x with -x and y with -y. The equation becomes (-y)^2-(-y x -x)=2, which simplifies to y^2+xy=2. This is different from the original function, so there is no origin symmetry.Learn more about Symmetry of Functions here:https://brainly.com/question/16710816
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What is the domain of the function f(x)= 1/3x+2
The answer is the last one
x≥-6
I hope this helps, and God bless <3
The length of a rectangle is given by 5t+4sqrt(t), and its height is sqrt(t), where t is time in seconds and the dimensions are in centimeters. Fine the rate of change of the area of the rectangle with respect to time when the length of the rectangle is 9 centimeters.
Answer:
11.5 cm²/s
Step-by-step explanation:
We must solve two problems to answer this question:
find the time at which the length is 9 cmfind the rate of change of area with respect to time (at that time)For the first problem, we have ...
... 9 = 5t +4√t
... 9 -5t = 4√t . . . . . subtract 5t
... 81 -90t +25t² = 16t . . . . square both sides
... 25t² -106t +81 = 0 . . . subtract 16t
... (t -1)(25t -81) = 0 . . . . factor
... t = 1 or 3.24 . . . . . . t=3.24 is an extraneous solution
_____
For the second problem, we have area (a(t)) is ...
... a(t) = length×height = (5t +4√t)(√t) = 5t^(3/2) +4t
Then the derivative is ...
... a'(t) = (3/2)(5√t) +4
and
... a'(1) = (3/2)(5√1) +4 = 11.5 . . . . . cm²/s
_____
Comment on the attachment
A graphing calculator can help solve both problems. It can help find the time at which length is 9 cm by solving ... length-9 = 0. (The nice thing here is that there is no extraneous solution.) It can compute the derivative of a function, too.
Jack is mowing a lawn that has a shed. Jack wants to know the area of the lawn he has to mow. here are the dimensions of the yard and the shed. 13x-4 length 5x withd shed is 2x+4length withd is 2x
find a polynomial that describes the area of the lawn he has to mow. i.e. find the area of the area of the shed.
We know that the formula for area is simply:
area = l w
where l is length and w is width
yard dimensions: l = 13x – 4, w = 5x
Ayard = (13x – 4) 5x = 65x^2 – 20x
shed dimensions: l = 2x + 4, w = 2x
Ashed = (2x + 4) 2x = 4x^2 + 8x
Therefore the area to mow is:
Amow = Ayard – Ashed
Amow = 65x^2 – 20x – (4x^2 + 8x)
Amow = 65x^2 – 20x – 4x^2 – 8x
Amow = 61x^2 – 28x
Joshua earns $8.20 per hour when he works at the college library. How much money does he earn by working at the library for $4.5 hours.
PLEASE HELP!!!
Tina has put 15 of her old CDs in a storage crate. How many more CDs can she store in the crate if it can hold no more than 23 CDs
Ahmad is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 12 feet and its width is 10 feet. Suppose each bag of fertilizer covers 30 square feet. How many bags will he need to cover the garden?
which of the following steps were applied to abc obtain a'b'c'
Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
Given are two triangles
ABC is having vertices as (4,6) (7,6) and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
On comparing the vertices corresponding we find a certain pattern.
X coordinate is reduced by 2 and y coordinate is increased by 4.
This implies the transformation is
Shifted 2 units left and 4 units up
there are seven days how many days are there in 16 weeks
Find the simple interest. Principal $2300 rate 20% time 27 months The interest is $ ?