Answer:
88
Step-by-step explanation:
HELP WHATS THE ANSWER
Answer:
13.5
Step-by-step explanation:
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
There are 3 boys for every 4 girls in a class. If there are 16 girls, how many boys are there?
If there are 3 boys for every 4 girls in a class, there would be 12 boys because 16 ÷4 us 4, and 4×3 is 13.
Help me pleaseeeeeeeeeeeeeeeeeeeee
Answer:
its the 4/7x 28
Step-by-step explanation:
you count by 2 and then you look for the numbers
Answer:
THE OTHER PERSON IS WRONG DO NOT LISTEN YOUNG ONE
Step-by-step explanation:
THE ANSWER IS D, 2/7 x 28
Read the proof.
Given: AB ∥ DE
Prove: △ABC ~ △EDC
Triangles A B C and E D C connect at point C. Sides A B and D E are parallel.
Statement Reason
1. AB ∥ DE 1. given
2. ∠ACB and ∠ECD are vert. ∠s 2. definition of vertical angles
3. ∠ACB ≅ ∠DCE 3. vertical angles are congruent
4. ∠BDE and ∠DBA are alt. int. ∠s 4. definition of alternate interior angles
5. ∠BDE ≅ ∠DBA 5. alternate interior angles are congruent
6. △ABC ~ △EDC 6. ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem
Answer:
Its AA similarity theorem
Step-by-step explanation:
correct on edge 2021
The triangles ABC and EDC are similar by AA similarity theorem.
What is similarity in triangles?Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.
Given is a proof of showing △ ABC ~ △ EDC
The proof is as follows :-
Statement Reason
AB ∥ DE Given
∠ ACB = ∠ ECD definition of vertical angles
∠ BDE ≅ ∠ DBA alternate interior angles are congruent
△ ABC ~ △ EDC AA similarity theorem
AA similarity theorem :-
AA similarity theorem states that when two corresponding angles of two triangles are found congruent then the triangles are similar by AA similarity theorem.
Hence, the missing reason is AA similarity theorem.
For more references on AA similarity theorem, click;
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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!
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)
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
m(x)=x2+4x n(x)=x
(mn)(x)=
A.) x2+4x(x)
B.) (x2+4x)(x)
Answer:
b is correct
Step-by-step explanation:
The product of the functions M(x) and n(x) is x³+ 4x².
To find the product of the two functions, M(x) = x² + 4x and n(x) = x, we need to multiply them together.
So, (mn)(x) = M(x) × n(x)
Substituting the given functions:
(mn)(x) = (x² + 4x) × x
Now, we can simplify the expression by applying the distributive property of multiplication:
(mn)(x) = x × x² + x × 4x
Simplifying further:
(mn)(x) = x³ + 4x²
Therefore, the product of the functions M(x) and n(x) is x³+ 4x².
Learn more about Polynomial here:
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15 quarts=_cups how many cups???
The measure of one side of a square is (s - 3) inches long. Which pair of expressions both represent the perimeter of this square?
a) 2s + 3 and (s + 3) + (s + 3)
b)2(s + 3) and (s + 3) + (s + 3)
c) 4s + 3 and (s + 3) + (s + 3) + (s + 3) + (s + 3)
d) 4( + 3) and (s + 3) + (s + 3) + (s + 3) + (s + 3)
The measure of one side of a square is (s + 3) inches long. The pair of expressions which both represents the perimeter of this square is:
d) 4( s + 3 ) and (s + 3) + (s + 3) + (s + 3) + (s + 3)
simiply the following (-4)⁶÷(-4)³.i will mark as brainlest
a = 7 and 10 – a = 3
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.
The last answer choice is 53 please answer
Answer:
Step-by-step explanation:
Chen is 44 inches tall
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:
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
Target is having black Friday deals Alma enLG 50 TV cost $330 and it is on sale for 30% off what is the sale price of the TB after the discount in excluding tax
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.
algebra 1- pls help! (I messed up previous question so I’m retyping it-)
Solve for x
-8x+14 ≥60 OR -4x+50 -2
B.) x ≤ -23/4
C.) x>-2
D.) There are no solutions
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.
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
Which of the following is an example of discrete data?
Temperature (in Fahrenheit) of teh Pacific Ocean at Huntington Beach
Lifetime (in hours) of 35 fluorescent light bulbs
Amount of caffeine (in milligrams) for 8 ounces of popular drinks
Number of hamburgers sold each day at Hamburger Mary's
Weight of dogs (in pounds) at the Seal Beach Animal Care Center
Answer:
Number of hamburgers sold each day at Hamburger Mary's because it's counting a number of something, not measuring a quantity with respect to a variable like temperature or weight. If this is still unclear let me know what I need to clarify. Have a nice night.
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
Find the X- and y-intercept of the line -7/5x - 4y=7
Answer:
-7 and 7
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
Hello :) pls help thank you very much!
......................
Answer:
Given: That's exactly what we've been givenCombine Like TermsSubtraction property of equality: We subtract 12 from both sides of the equation.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.
can someone help me like ion get it
Answer:
D is the correct answer.
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