Answer:
to find the answer for 1 pencil you just need to divide
Step-by-step explanation:
3.20$ divide by 4=0.8 /each pencil cost 0.8
4.80$ divide by 12=0.4 /each pencil cost 0.4
a = 7 and 10 – a = 3
An artifact is four times 4 times older than an antiuqe book. In 200 years the artifact will be 3 times older than the book. How old is the artifact now?
Answer:
The present age of the artifact is 1,600 years
Step-by-step explanation:
let the present age of the artifact = x
let the present age of the book, = y
x = 4y ---- equation (1)
x + 200 = 3(y + 200) ------equation (2)
x + 200 = 3y + 600
substitute in the value of x into the equation;
4y + 200 = 3y + 600
4y - 3y = 600 - 200
y = 400
Then, x = 4 x 400
x = 1,600 years
Therefore, the present age of the artifact is 1,600 years
Answer:
The present age of the artifact is 1,600 years
Step-by-step explanation:
let the present age of the artifact = x
let the present age of the book, = y
x = 4y ---- equation (1)
x + 200 = 3(y + 200) ------equation (2)
x + 200 = 3y + 600
substitute in the value of x into the equation;
4y + 200 = 3y + 600
4y - 3y = 600 - 200
y = 400
Then, x = 4 x 400
x = 1,600 years
The image of the point (7,-4) under a translation is (12,-5). Find the coordinates
of the image of the point (-8, -3) under the same translation.
The third term of a geometric progression is 63/4 and the sixth term is 1701/32. Find the sum of the first 12 terms of the sequence.
Answer:
The sum of the first 12 terms of the sequence is 2703.673096
Step-by-step explanation:
The nth term of a geometric progression is a(n) = [tex]ar^{n-1}[/tex], where
a is the first termr is the common ratio between each two consecutive termsThe sum of n terms of the geometric progression is s(n) = [tex]\frac{a(r^{n}-1)}{r-1}[/tex]
∵ The third term of a geometric progression is [tex]\frac{63}{4}[/tex]
∴ a(3) = [tex]\frac{63}{4}[/tex]
∵ a(3) = ar²
→ Equate its two right sides
∴ ar² = [tex]\frac{63}{4}[/tex] ⇒ (1)
∵ The sixth term is [tex]\frac{1701}{32}[/tex]
∴ a(6) = [tex]\frac{1701}{32}[/tex]
∵ a(6) = a[tex]r^{5}[/tex]
→ Equate its two right sides
∴ a[tex]r^{5}[/tex] = [tex]\frac{1701}{32}[/tex] ⇒ (2)
→ Divide (2) by (1)
∴ r³ = [tex]\frac{27}{8}[/tex]
→ Take ∛ for both sides
∴ r = [tex]\frac{3}{2}[/tex] = 1.5
→ Substitute the value of r in (1) to find a
∵ a(1.5) = [tex]\frac{63}{4}[/tex]
∴ 1.5a = 15.75
→ Divide both sides by 1.5
∴ a = 10.5
→ Let us find the sum of the first 12 terms
∵ n = 12, a = 10.5, and r = 1.5
→ Substitute them in the rule of the sum above
∵ s(12) = [tex]\frac{10.5(1.5^{12}-1)}{1.5-1}[/tex]
∴ s(12) = 2703.673096
∴ The sum of the first 12 terms of the sequence is 2703.673096
10z^2 -2z-2 10z 2 −2z−2
z =(2-√-116)/-20=1/-10+i/10√ 29 = -0.1000-0.5385i
z =(2+√-116)/-20=1/-10-i/10√ 29 = -0.1000+0.5385i
Step-by-step explanation:
a new recipe calls for 1/3 cups sugar and you have 2 1/3 cups in the pantry if you have unlimited supplies of the other ingredients how many recipes could you make? PLS HELP
Answer:
7 recipes could be made with [tex]2\frac{1}{3}[/tex] cups of sugar.
Step-by-step explanation:
Quantity of sugar required for a recipe [tex]=\frac{1}{3}[/tex] cups
Quantity of sugar required in a pantry [tex]=2\frac{1}{3}[/tex] cups
Here,
[tex]2\frac{1}{3}=\frac{7}{3}[/tex]
So,
Quantity of sugar required in a pantry [tex]=\frac{7}{3}[/tex] cups
Number of recipes that could be made [tex]=\frac{\frac{7}{3} }{\frac{1}{3} } =7[/tex]
Therefore, 7 recipes could be made with [tex]2\frac{1}{3}[/tex] cups of sugar.
Please help (look at the picture)
15 quarts=_cups how many cups???
Lara went to the nursery and spent $140 she purchased 4 plants each of the plant costs the same price what is the cost of 1 plants ?
Answer:
$35 per plant
Step-by-step explanation:
You take the 140 and divide that by 4 to get your answer.
Lenny makes $55,000 and is getting annual raises of $2,500. Karl makes $62000, with
annual raises of $2,000. How many years will it take for Lenny and Karl to make the
same salary?
Step-by-step explanation:
let no of years be x.
55000 + 2500x = 62000 + 2000x
500x = 7000
x = 14
therefore, 14 years.
Topic: algebraic eqns
If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!
The lengths of the sides of a triangular sign are x inches, (4x - 5) inches, and (7x+8) inches. What is the perimeter of the sign?
The perimeter of the sign is in.
(Simplify your answer Do not factor)
Answer:
The perimeter of triangular sign is 12x+3
Step-by-step explanation:
Length of side1 of triangle = x inches
Length of side2 of triangle = 4x-5 inches
Length of side3 of triangle = 7x+8 inches
We need to find perimeter of triangular sign.
The formula used is: [tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides[/tex]
Now, finding perimeter of triangular sign:
[tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides\\Perimeter \ of \ triangle = x+4x-5+7x+8\\Perimeter \ of \ triangle = x+4x+7x-5+8\\Perimeter \ of \ triangle = 12x+3[/tex]
The perimeter of triangular sign is 12x+3
HELP WHATS THE ANSWER
Answer:
13.5
Step-by-step explanation:
I Four men can dig
a pit in 5 days,
men can do the same job
in 2 days
How many
Answer:
7?
Step-by-step explanation :
yo creo que si
Just answer it plzzzzz
Answer:
i would say answer A
Step-by-step explanation:
Two groups of people, the Yellow Group and the Orange Group, suddenly find themselves in a world where there are only two 'production opportunities': pumping water and picking berries.
After a little while the Yellow Group has learned that it seems to produce about 2 gallons per hour while pumping water and about 8 berries per hour while picking.
Meanwhile the Orange Group has learned that it seems to produce about 1 gallon per hour while pumping water and about 3 berries per hour while picking.
If we were able to make production decisions that were efficient from the perspective of both groups combined, what would we consider to be the opportunity cost of producing one gallon of water?
3 berries
4 berries
25 cents
33⅓ cents
Answer:
3 berries
Explanation:
Opportunity costs for the Orange group:
Opportunity cost of pumping 1 gallon of water = 3/1 = 3 berries
Opportunity cost of picking 1 berry = 1/3 = 0.333 gallons of water
Opportunity costs for the Yellow group:
Opportunity cost of pumping 1 gallon of water = 8/2 = 4 berries
Opportunity cost of picking 1 berry = 2/8 = 0.25 gallons of water
Opportunity cost for both groups combined:
Opportunity cost of pumping 1 gallon of water = 3 berries (Orange group should pump water since opportunity cost is lower)
Opportunity cost of picking 1 berry = 0.25 gallons of water (Yellow group should pick berries since opportunity cost is lower)
Opportunity costs are the extra costs or benefits lost resulting from choosing one investment or activity over another alternative. In this case, people can either pump water or pick berries, but they cannot do both at the same time. When they are pumping water, the opportunity cost is the amount of berries that they will not be able to collect, and vice versa.
What is 14.724 rounded by the nearest hundredth
Answer:
14.72
Step-by-step explanation:
describe the inequality 5x>4x+7 in words
Answer:
five times a number is greater than the sum of four times that number and seven
PLEASE HELP 40 POINTS!!!, I DO NOT KNOW HOW TO DO THIS AT ALL
Answer:
ill Put the answer in the comments if you give a pic of the image for this problem
Step-by-step explanation:
Which best describes the relationship between the successive terms in the sequence shown?
2.4, –4.8, 9.6, –19.2
(A)The common difference is –7.2.
(B) The common difference is –2.4.
(C)The common ratio is –2.0.
(D)The common ratio is –0.5.
Answer:
(C)The common ratio is –2.0Step-by-step explanation:
Given sequence:
2.4, –4.8, 9.6, –19.2This is not AP as the difference in terms is not common
This is GP with the common ratio of -2 as:
-19.2/9.6 = 9.6/ -4/8 = -4.8/2.4 = -2Correct choice is (C)
What is the answer to -4 x ( -6 )
Answer:
24x
Step-by-step explanation:
Multiply − 6 by − 4 .
Answer:
24
Step-by-step explanation:
you multiply negative 4 by negative 6
Which expression is equivalent to cos(40°)cos(10") + sin(40°)sin(10º)?
O sin(40° – 10°)
O cos(40° + 10º)
O sin(40° + 10º)
O cos(40° – 10º)
Answer:
The equivalent expression is cos(40° – 10º) ⇒ D
Step-by-step explanation:
The rule of cosine the compound angles is
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
Let us use these rules to solve the question
∵ cos(40°)cos(10°) + sin(40°)sin(10º)
∵ The middle sign is plus
∴ We will use the 2nd rule above
→ Compare the rule by the given expression to find the value of A and B
∵ A = 40° and B = 10°
∴ cos (A - B) = cos (40° - 10°)
∴ cos (40° - 10°) = cos(40°)cos(10°) + sin(40°)sin(10º)
∴ The equivalent expression is cos(40° – 10º)
Find the X- and y-intercept of the line -7/5x - 4y=7
Answer:
-7 and 7
Step-by-step explanation:
During one day in a hardware store, 37 people came in and made a purchase, and 13 people looked around but didn’t purchase anything. Express the following in ratios:
a. Purchasers to nonpurchasers
b. Nonpurchasers to purchasers
c. Purchasers to total customers
d. Nonpurchasers to total customers
The last answer choice is 53 please answer
Answer:
Step-by-step explanation:
Chen is 44 inches tall
A company can produce 60 million chocolate candies within a 24-hour period.
Part A
Using this rate, create an equation to represent the number of chocolate candies,
c
, in millions, the company can produce in
h
hours.
Answer:
f(x)=60c * 24h
Step-by-step explanation:
Hope this helped!
Juice is sold in small bottles and large bottles.
The volume of the large bottle is 1125 ml.
1125 ml
volume of small bottle : volume of large bottle = 2:5
A cafe has small glasses and large glasses.
volume of small glass : volume of large glass - 4:7
A small bottle fills 6 smal glasses with no juice left over.
How many large glasses can be filled by a large bottle?
You must show your working out
Answer:
8 large glasses can be filled by a large bottle.
Step-by-step explanation:
First we calculate the volume of a small bottle:
[tex]\frac{SmallBottle}{1125}=\frac{2}{5}[/tex]Volume of small bottle = 450 mLNow we calculate the volume of a small glass:
" A small bottle fills 6 small glasses with no juice left over.", this means that
Volume of small glass = volume of small bottle / 6Volume of small glass = 450 / 6 = 75 mLThen we calculate the volume of a large glass:
[tex]\frac{75}{LargeGlass}=\frac{4}{7}[/tex]Volume of large glass = 131.25mLFinally we divide the volume of a large bottle by the volume of a large glass:
[tex]\frac{1125}{131.25}= 8.5[/tex]So 8 large glasses can be filled by a large bottle with juice left over.
can someone help me ASAP??? 49 POINTS!!!!!!!!!
John has 600 marbles and he is giving to his friends. he gives 1/5 of them to bob, 8% to pat, and 75 to matt. How many marbles does John have left?
Answer:
John has 357 marbles left.
Step-by-step explanation:
120 marbles went to Bob
48 went to Pat
and 75 to Matt.
4/7 divided by 4 ( simplest form)
Answer:
1/7 Brainliest plz
Step-by-step explanation:
What is the factorization of the trinomial below?
2x2 + 11x+15
A. (2x + 1)(x +15)
B. (2x+15)(x + 1)
C. (2x+3)(x+5)
D. (2x+5)(x+3)
SUBMIT
Answer:
D
Step-by-step explanation:
Just took the test
In the diagram, Triangle ABC ~ Triangle ACD. If AD = 12 and DB = 15, What is AC?
Answer:
9
Step-by-step explanation:
DB^2=AD^2+AC^2
15^2=12^2+AC^2
AC^2=225-144
AC^2=81
AC=√81
AC=9