Answer: The students can be divided into 7 groups.
Each group will have 3 boys and 8 girls.
Step-by-step explanation:
There are 21 boys and 56 girls.
To divide them so that each group has the same number of both boys and girls.
We find GCD(21,56).
21 = 3 x 7
56 = 2 x 2 x 2 x 7
GCD (21,56) = 7
So, the students can be divided into 7 groups.
Number of girls in each group = [tex]\dfrac{56}{7}=8[/tex]
Number of boys in each group = [tex]\dfrac{21}{7}=3[/tex]
So, each group will have 3 boys and 8 girls.
The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap
Sum of 8th & 4th terms of an AP = 24
Sum of 6th & 10th terms = 44
Find:A.P.
Solution:We know that,
nth term of an AP = a + (n - 1)d
Hence,
⟹ a + (8 - 1)d + a + (4 - 1)d = 24
⟹ a + 7d + a + 3d = 24
⟹ 2a + 10d = 24 -- equation (1)
Similarly,
⟹ a + 5d + a + 9d = 44
⟹ 2a + 14d = 44 -- equation (2)
Subtract equation (1) from (2).
⟹ 2a + 14d - (2a + 10d) = 44 - 24
⟹ 2a + 14d - 2a - 10d = 20
⟹ 4d = 20
⟹ d = 20/4
⟹ d = 5
Substitute the value of d in equation (1).
⟹ 2a + 10(5) = 24
⟹ 2a = 24 - 50
⟹ 2a = 24 - 50
⟹ 2a = - 26
⟹ a = - 26/2
⟹ a = - 13
We know,
General form of an AP is a , a + d , a + 2d...
Hence,
⟹ required AP = - 13 , - 13 + 5 , - 13 + 2(5)...
⟹ required AP = - 13 , - 8 , - 3....
I hope it will help you.
Regards.
Does the graph show a proportional
relationship? If so, use the graph to find
the constant of proportionality.
Answer:
yes. y-=25x
Step-by-step explanation:
Answer:
its 40
Step-by-step explanation:
Aanya wrote the four equations that are shown below.
A
6 x minus 8 = 4 (x minus 2) + 2 x
B
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
C
7 x + 2 minus x = 6 (x + 2)
D
4 (x + 3) + x = 5 (x + 1) + 7
She examined them, without solving them, to determine which has exactly one solution. Which of Aanya’s equations has exactly one solution?
6 x minus 8 = 4 (x minus 2) + 2 x
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
7 x + 2 minus x = 6 (x + 2)
4 (x + 3) + x = 5 (x + 1) + 7
Answer:
B
Step-by-step explanation:
.' )
Answer:
The answer is B.
Step-by-step explanation:
I just took the test.
Which two ratios form a proportion?
3:4 and 6:12
3:4 and 9:15
3:4 and 12:18
3:4 and 15:20
Answer:
3:4 and 15:20
Step-by-step explanation:
The answer is the fourth one because 3:4 and 15:20 are equivalent, so there's your answer. Hope it helps!
Compare the ratio of miles driven to gallons of gas used for Car A and Car D. Write the ratios as fractions and use a common denominator of 8. The ratio of miles to gallons for Car A is /8. The ratio of miles to gallon for Car D is /8. The ratio for Car A is the ratio for Car D.
Answer:
The ratio of miles to gallons for Car A is
✔ 224
/8.
The ratio of miles to gallon for Car D is
✔ 184
/8.
The ratio for Car A is
✔ greater than
the ratio for Car D.
Step-by-step explanation:
Landon is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.80 for every minute of use. Write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.
Answer:0.80t+10
Step-by-step explanation:
Diana is buying plates and cups for a party. She wants the same number of each. Plates are sold in packs of eight and cups are sold in packs of 12. What is the least number of plates and cups she can buy? How many packs of plates? How many packs of cups? Explain how you know.
Answer:
What is the least number of plates and cups she can buy?
The least number of cups of plates and cups she can buy is 24
How many packs of plates?
3 packs of plates
How many packs of cups?
2 packs of cups
Step-by-step explanation:
What is the least number of plates and cups she can buy?
We solve this using the Lowest Common Multiple method
The L.C.M of 8 and 12
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 12: 12, 24, 36, 48
Therefore,
LCM(8, 12) = 24
Hence, the least number of cups and plates she can buy is 24
How many packs of plates?
Plates are sold in packs of eight
Hence: 24 ÷ 8 = 3 packs of plates
How many packs of cups?
Cups are sold in packs of 12
Hence: 24 ÷ 12 = 2 packs of cups
What is 4 divided by 3/5
Answer:
20/3 or 6 2/3
Step-by-step explanation: 4/1 times 5/3 multiply and you get 20/3
Answer:
6 2/3
Step-by-step explanation:
20 POINTS!! HELP ME PLZZ I NEED HELP WITH THIS!!
Answer:
0.22222222
Step-by-step explanation:
Hope this helps!!!
Answer:
0.22222222
Step-by-step explanation:
you have to divide 2 by 9.
please help me? im desperate!
Answer:
The same sign
Step-by-step explanation:
WHAT IS THE LAST SENTANCE FOR DESPASITO IN ENGLISH!!!!!!!!!!!!!!11
-1/3(x-15)=-4 what is the correct sequence of operations
Answer:
x = 3
Step-by-step explanation:
The steps I show will be listed from first-to-last.
-1/3x + 5 = -4 (Distribute)
-1/3x = -9 (Subtract 5 from both sides)
x = 3 (Multiply both sides by -3)
Someone please help only answer if your 100 percent sure
Answer:
90
Step-by-step explanation:
The given measurement of a surface Area of a sphere is 196π.Find it's radius
(thanks in advance)
Answer:
Hope this solution helps you. Sorry for the handwriting .
A student solved the equation below using the steps shown, rounding to two decimal places if necessary.
which step contains the first mistake ?
A. step 2
B. step 1
C. step 3
D. step 4
Answer:
Step 1
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line shown on the graph?
If AABC = ADEC,
ZB = 2x + 31 and ZE = 7x - 24
A
D
B
E
x = [?]
/_ b = /_ e
2x + 31 = 7x - 24
5x = 55
x = 11
there are 48 newborn girls in a hospital nursery. For every 3 girls, there are 2 boys. How many newborn babies are in the nursery?
Hi! I believe your answer is 80 newborn babies. To find the number of boys, divide 48 by 3 (since it is for every 3 girls) and you'll get 16. Next, multiply 16 and 2 (for every 2 boys) and you'll get 32. Lastly, add 48 and 32 and you'll get the number of newborn babies in the nursery (80). I hope this helps you! Good luck and have a great day. ❤️✨
Number of total newborn babies = 80
What is ratio?A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.
Given,
Total number of girls = 48
For every 3 girls, there are 2 boys.
Ratio of girls to boy = 3/2
Let there are x boys,
then,
48/x = 3/2
3x = 96
x = 32
Number of boys = 32
Total newborn babies = Number of girls + number of boys
= 48 + 32 = 80
Hence, 80 newborn babies are in nursery.
Learn more about ratio here:
https://brainly.com/question/1504221
#SPJ2
What is the correct equation to find the value of X?
Answer:
x = 12
Step-by-step explanation:
The 2 angles shown are corresponding angles and congruent, thus
8x - 17 = 5x + 19 ( subtract 5x from both sides )
3x - 17 = 19 ( add 17 to both sides )
3x = 36 ( divide both sides by 3 )
x = 12
Need helps with 45 , picture above
Answer:
Ok:
Step-by-step explanation:
We know Josh buys 3 oranges for $2 and sells 2 oranges for $3. Let's take the LCM (least common multiple) of 2 and 3. It is 6. If he buys 6 oranges, he needs $4. When he sells 6 oranges he makes $9. That is a total profit of $5. In total that means, if we multiple by 10, that means that if he sells 60 oranges, he would make $50. Thus C is the answer
CAN SOMEONE HELP ME PLEASE ?!
Answer:
A. XY
Step-by-step explanation:
The answer is XY because it is the same length as XZ. I didn't determine this by guessing, but by eliminating the wrong answer choices. The tick marks indicate what lines are congruent to each other. The answer can't be C because AY is congruent to YC since they both have 3 tick marks, indicating that they are congruent to each other. Same goes for the others.
The total cost after tax to repair Deborah's computer is represented by 0.09(60h)+60h, where h represents the number of hours it takes to repair Deborah's computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answer:
0.09(60h)
Step-by-step explanation:
The part that represents the tax is 0.09.
This is because, we can rewrite the sum as;
Amount of tax + Total cost for the number of hours
Now, the amount of tax can only be a percentage of the total
We can write 0.09 as 9/100
This can be interpreted as 9% of the total amount
So therefore we can rewrite the amount as;
9% of 60h + 60h
So the part that represents the amount of tax Deborah has to pay is 0.09(60h)
The regular price of a baseball hat is $15.65. If Julio buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?
please help me with this
Larry is putting a row of rocks around his rectangular pool. Which descriptive model will tell him how many rocks he needs?
[2(pool length) + 2(pool width)] times the width of the rocks
(pool length times pool width) times the width of the rocks
(pool length times pool width) divided by the width of the rocks
[2(pool length) + 2(pool width)] divided by the width of the rocks
Answer:
P = [2( l)+2(w)] / width of the rock
Step-by-step explanation:
row of rocks around his rectangular pool, this tells us we are finding the perimeter
The perimeter of a rectangle is given by
P = 2( l+w)
P = 2( l)+2(w)
But we know that the length takes into account the width of the rock so divide each side by the width of the rock
P = [2( l)+2(w)] / width of the rock
can anyone pls helppppp
A ball is thrown strait up from the top of a 64 foot tall building with an initial speed of 48 feet per second. The height of the ball as a function of time can be modeled by the function h(t)=-16t^2+48t+64. At what other time will the ball be at a height of 64 feet? How long will it take for f ball to reach its maximum height? What is he maximum height reached by the ball? How long willlit take for the ball to hit the ground?
Answer:
see below
Step-by-step explanation:
h(t)=-16t^2+48t+64
Find when h(t) = 64
64 = -16t^2+48t+64
Subtract 64 from each side
0 = -16t^2+48t
Factor
0 = -16t( t-3)
Using the zero product property
-16t =0 t-3 =0
t=0 and t=3
Other than at t=0, so at t=3 seconds
How long will it take for f ball to reach its maximum height?
Find the vertex
t = -b/2a = -48 / ( 2 * -16) = -48/ -32 = 1.5 seconds
It will reach the maximum height at 1.5 seconds
What is the maximum height reached by the ball?
The height will be
h(1.5) = -16*(1.5)^2+48(1.5)+64
= -36+72+64
= 100
The maximum height is 100 ft
How long will it take for the ball to hit the ground?
h(t) =0
0=-16t^2+48t+64
Factor
0 = -16( t^2 - 3t -4)
0=- 16( t-4) (t+1)
Using the zero product property
t-4=0 t+1=0
t =4 t = -1
Since time cannot be negative
t=4 seconds
Katie wants to buy a bracelet. She only has $30 to spend. She has found a bracelet with a regular price of $45 and a discount of 35%. If the sales tax is 7%, will she have enough to buy the bracelet? If so, how much money will Katie have left? If not, how much more money will she need?
Given :
Money Katie has, M = $30.
She has found a bracelet with a regular price of $45 and a discount of 35%.
The sales tax is 7%.
To Find :
Will she have enough to buy the bracelet.
Solution :
Original price = $45 .
Price after discount = $( 45 - 45×0.35) = $29.25 .
Selling Price = $( 29.25 + 29.25×0.07 ) = $31.2975 .
Since, selling price is greater than $30.
Money needed = $( 31.2975 - 30 ) = $1.2975 .
Therefore, Katie will not buy the bracelet.
A person invests 1000 dollars in a bank. The bank pays 6% interest compounded
monthly. To the nearest tenth of a year, how long must the person
leave the money
in the bank until it reaches 3300 dollars?
Answer:
t=19.94841\approx 19.9 \text{ years}
t=19.94841≈19.9 years
Step-by-step explanation:
what is faster drive a car that goes 40 k per hour
or
a car that goes 15 meters per second
Answer:
40k per hour is faster
mark me as branliest plz