This geometric progression has 5 terms
This is a geometric progression or geometric series whose sum of n terms is given by the formula
Sn = a[([tex]r^{n\[/tex] – 1)/(r – 1)]
Where Sn is sum of n terms of geometric progression, a is the first term of the series , r is the common ratio
Here we are required to find the number of terms in the geometric progression whose first term is -3 and common ratio is 6
-4665 = -3 [( [tex]6^{n}[/tex]-1)/(6-1)
1555=( [tex]6^{n}[/tex]-1)/5
7775= [tex]6^{n}[/tex]- 1
7776 = [tex]6^{n}[/tex]
[tex]6^{5}[/tex] = [tex]6^{n}[/tex]
So, n=5
Therefore this geometric progression has 5 terms
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nikola competed in an aquathon (swimming and running) competition. he swam at a rate of km/hr and ran at a rate of km/hr for a total distance traveled of km. if he completed the race in hours, how long did he take to complete each part of the race?
Nikola took 2 hours to finish the swimming part
Nikola took 4.5 hours to finish the running part
Define Algebra?A form of arithmetic in which the rules of arithmetic are used to combine letters that represent numbers.
Calculations:
Assume,
[tex]t=time\;in\;hrs\;to\;complete\;swimming\;part[/tex]
[tex]6.5-t=time\;in\;hrs\;to\;complete\;running\;part[/tex]
[tex]d=distance\;in\;km\;that\;he\;swam[/tex]
[tex]73.5-d=distance\;in\;km\;that\;he\;ran[/tex]
Equation of swimming part,
[tex]d=3t[/tex]
Equation of running part.
[tex]73.5-d=15\times(6.5-t)[/tex]
Substitute the value of d in running part equation,
[tex]73.5-3t=15\times(6.5-t)[/tex]
[tex]73.5-3t=97.5-15t[/tex]
[tex]12t=24[/tex]
Therefore,
[tex]t=2[/tex]
[tex]Time\;to\;complete\;summing\;part=t[/tex]
[tex]Time\;to\;complete\;summing\;part=2\;hours[/tex]
[tex]Time\;to\;complete\;summing\;part=6.5-t[/tex]
[tex]Time\;to\;complete\;summing\;part=6.5-2[/tex]
[tex]Time\;to\;complete\;summing\;part=4.5\;hours[/tex]
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eight concrete specimens are constructed from a new formulation, and the compressive strength of each is measured.
The populace is the concrete produced by a certain procedure. This population is conceptual since the concrete won't exist until the sampling procedure has created it.
What is the difference between tangible and conceptual population?
It is frequently crucial to ascertain the type of population we are working with when asked to perform a sample of it. Sometimes we want to learn more about a lot of different things, like people, apple trees, cereal boxes, etc. Physical things make up the majority of this population. But occasionally, we work with a population that is determined by how well a certain method works (like flipping a coin). We cannot influence that population, but we are aware of its behavior. The population is the broad category of topics about which we are interested in learning more. Since we are dealing with concrete objects that we can touch and interact with, it is more particularly a tangible population.
Similar to the bag of marbles, we have a 50/50 probability of seeing each result. The population does not yet exist with the coin, which is the problem. To get a result, we must flip a coin. Although it is only a notional population, we nonetheless regard "all of the coin flips" as the conceptual population.
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Please help me out with my homework I am struggling
Answer:
v = 72
Step-by-step explanation:
If the length of both the sides are 12, it means it is an Isosceles triangle which means 2 sides of a triangle are equal. If both sides are equal then both angles will be equal too.
54 and 54
54 + 54 + v = 180
108 + v = 180
v = 72
Factorise a^2/8 - b^2/18
Step-by-step explanation:
answer=((a/(2× sqrt 2))+(b/(3× sqrt)))((a/(2× sqrt 2))-(b/(3× sqrt 2)))
method-difference of two squares
Can Someone please help me with this question? I really need help. It Is Algebra 1 and I'm not very good at it. I'm trying to pass with a B or better.
D. The solution of the quadratic equation using completing the square method is x = 7 ±√3.
What is completing the square method?Completing the square method is one of the methods to find the roots of the given quadratic equation.
In completing the square method, we have to convert the given equation into a perfect square.
The given quadratic equation;
x² - 14x + 46 = 0
collect similar terms together;
x² - 14x = -46
take half of coefficient of "x", square it and add it to both sides of the equation.
(x - 7)² = -46 + 49
(x - 7)² = 3
take square root of both sides
x - 7 = ±√3
add "7" to both sides of the equation
x = 7 ±√3
Thus, the solution of the quadratic equation using completing the square method is x = 7 ±√3.
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Name the property that is used in 5 ⋅ n ⋅ 2 = 0 . Then find the value of n.
Answer: Zero product property
n = 0
=========================================
Explanation:
The zero product property is the idea that if A*B = 0, then either A = 0 or B = 0 or both are zero.
This is because we cannot multiply nonzero values to get a result of zero.
In the equation 5*n*2 = 0, we have 5 and 2 as nonzero, which forces the variable n to be zero. So this is why n = 0 is the only solution here.
-----------------
Extra info:
The zero product property is often used in factoring. For example, x^2+5x+6 = 0 factors to (x+3)(x+2) = 0. Then we set the pieces equal to zero and solve for x
x+3 = 0 leads to x = -3
x+2 = 0 leads to x = -2
If a pharmacist combined 50-ml portions of thre syrups having specific graveties of 1.10, 1.25, and 1.32, what would be the specific gravity of the combined product?
The specific gravity of the combined product is 1.22
Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.
Given,
The total quantity of portion= 50 ml
Specific gravities of the three syrups = 1.10,1.25 and 1.32
Then,
The specific gravity of the combined product= [tex]\frac{1.10+1.25+1.32}{3}[/tex]
= 1.22
Hence, the specific gravity of the combined product is 1.22.
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Question 7(Multiple Choice Worth 1 points)
(02.01 MC)
One of the factors of 8x3 - 800x is
O 8x
Ox+10
Ox-10
O All of the above
The factor of the given expression 8x³ - 800x is (A) 8x.
What are the factors?A factor is a number that is multiplied by another number to produce the desired result. The answer to a multiplication puzzle is a product. Imagine multiplying the factors in a multiplication problem to get the answer. For instance, factors 2 and 4 add up to 8: Just two factors or a great many factors can affect a number.In mathematics, a factor is a number or algebraic expression that divides another number or expression evenly, leaving no remainder. Due to the fact that 12 ÷ 3 = 4 and 12 ÷ 6 = 2, respectively, they are factors of 12 as well.1, 2, 4, and 12 make up the remaining 12 factors.So, 8x³ - 800x:
8x³ - 800x ⇒ take the common8x(x² - 100)As a result, (A) 8x is the expression's factor.
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The correct question is given below:
Question 7(Multiple Choice Worth 1 point)
(02.01 MC)
One of the factors of 8x3 - 800x is
A. 8x
B. x+10
C. x-10
D.All of the above
This is due at the end of the day please help
Answer:
Step-by-step explanation:
the answer is 8
8 shipping cost
8 + X = Y
A clearly spelled-out statement on group participation presented to members before the group commences would be particularly important when?
It's crucial to start a topic off positively in a group discussion when you feel completely confident over your statements in order to create the correct momentum that will lead to a strong start and help you establish yourself as the group leader.
What are the qualities of a good leader?Confidence is by far the most crucial quality. A strong sense of self-assurance is essential for a leader. Self-conscious people are rarely effective leaders. A guy needs to have the self-assurance to tell people to follow him. The leader must have faith in his judgement and actions. An important trait in a leader is honesty. If someone wants to gain followers, they must exhibit honesty and integrity. A leader needs to be an excellent innovator. He must exercise creativity in his work. Most importantly, innovation ensures a group's or invention's continuous existence. Innovation is necessary for growth to occur.
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The ratio of the measures of the three sides of a triangle is 3: 7: 5 , and its perimeter is 156.8 meters. Find the measure of each side.
Answer:
31.36m, 73.2m, 52.3m respectively
Step-by-step explanation:
The product of an integer and a decimal number will never be an integer.
The statement that the product of an integer and a decimal number will never be an integer is false
How to determine the true statement?The statement is given as
The product of an integer and a decimal number will never be an integer.
The above statement is false.
Take for instance, we have
2 x 2.5
2 is an integer and 2.5 is a decimal number
The product is
2 x 2.5 = 5
5 is an integer
Hence, the statement that the product of an integer and a decimal number will never be an integer is false
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This one too pretty pleaseeeeee
Answer:
Please mark this answer as the brainliest, it would really mean a lot to me
Answer = 28 Degrees
Step-by-step explanation:
If the triangle has two sides that are the same, it is an isosceles triangle.
The rule for an isosceles triangle is "an isosceles triangle △ABC where AB = AC, we have ∠B = ∠C."
So in this case, it would be FE = FG, and ∠E = ∠G.
Divide
266 divided by 15
Hint: The remainder is not a decimal it is the number that is leftover and can no longer be divided
17. The remainder is 11
I showed my work here
https://witeboard.com/537d7850-38f8-11ed-b5a9-6540cf185f3a
Answer:
17, remainder 11
____________
Long Division[tex]Borrow\:6\:from\:the\:ones\:place\\=26\\= 26 - 15(15 \cdot 1)\\= 11\\Drop\:the\:borrowed\:6\\= 116\\= 116 - 105(15 \cdot 7)\\= 11\\\\Using\:the\:numbers\:we\:multiplied\:\:the\:divisor\:by,\\we\:got\:17.\:So\:our\:answer\:would\:be\:17\:with\:a\:remainder\:of\:11.[/tex]
____________
Follow the 3 steps:
➪ Hope this helps!
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➪ Have a great day.
Please help with problem 7
Answer:
D
Step-by-step explanation:
When 7 and 14 are divided by their respective co-ratios, both quotients come out to 2.3333333333333. This means that D forms a porportion.
Answer:
Step-by-step explanation:
The answer is D because 7/14=0.5 and so does 3/6
The graph of y = -x + 2 is negative
over the interval (4, ∞) and positive over the
interval (-∞, 4). What happens on the graph
when x = 4? Explain. MP.2
What happens when x = 4 is that the graph is equal to zero when x = 4.
How to Interpret Graph Intervals?
The information that we have is:
"The graph of y = -1/2x + 2 is is negative over the interval (4, ∞) and positive over the interval (-∞, 4)."
Now, if for values of x smaller than 4 the graph is negative and for values of x larger than 4 the graph is positive, this must be that the graph must crosses the x-axis at some point, then with only that information, we can conclude that the graph is equal to zero when x = 4.
But we could also test it with the equation:
y = -(1/2)*x + 2
if we replace the x with 4.
y = -(1/2)*4 + 2 = -2 + 2 = 0.
Then our previous hypothesis was correct.
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Select the correct answer. A graph plots two points at (negative 5, negative 3) and (10, negative 8) on the x y coordinate plane. A diagonal curve connects both points. What is the range of the function shown on the graph above? A. B. C. D.
Based on the given parameters, the range of the function is -8 < y < -3
How to determine the range of the function?We have the following endpoints on the graph of the function;
(x, y) = (-5, -3)
(x, y) = (10, -8)
A diagonal curve connects both points
Remove the x values to determine the range
y = -3
y = -8
-8 is less than -3
So, the range can be represented as
-8 less than y less than -3
Express less than using the inequality <
So, we have
Range: -8 < y < -3
Hence, the range of the function is -8 < y < -3
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Answer: your answer should be -8 < y < -3
Step-by-step explanation:
For a college chemistry experiment, students need to prepare a solution containing ethylene glycol. They are each given 20 fluid ounces of a solution containing 2% ethylene glycol, to which they will add another solution that contains 12% ethylene glycol. How much of the 12% solution should they add to obtain a 5% ethylene glycol solution?
Students should add 8.6 fluid ounces of 12% ethylene glycol.
Using the relation between concentration and volume of solution to find the required amount of 12% ethylene glycol to be used. Let the required amount of 12% ethylene glycol be x fluid ounces. Forming the relation as follows -
C₁ × V₁ + C₂ × V₂ = C₃ × V₃
C₁ and V₁ represents 2% ethylene glycol, C₂ and V₂ represents 12% ethylene glycol and C₃ and V₃ represents 5% ethylene glycol solution. As V₂ is x, so, V₃ will be (20 + x).
Keep the values in formula to find the value of x
2%×20 + 12%×x = 5%×(20 + x)
Solving the equation for the value of x
2/100×20 + 12/100×x = 5/100×20 + 5/100×x
0.4 + 0.12x = 1 + 0.05x
Rearrange the equation -
0.12x - 0.05x = 1 - 0.4
Performing subtraction on both sides -
0.07x = 0.6
Shifting 0.07 to Right Hand Side and performing division
x = 0.6 ÷ 0.07
x = 8.6 fluid ounces
Hence, 8.6 fluid ounces of the 12% ethylene glycol should be added.
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SHOW WORK!!!!!!!!!!!!!!!!
AC = x +3, BC= 8, and AB= 2x-11. Find X
ABC are collinear. Point B is between A and C
Answer:
[tex]{ \rm{ac = ab + bc}} \\ { \rm{(x + 3) = (2x - 11) + 8}} \\ { \rm{2x - x = 3 + 11 - 8}} \\ { \rm{x = 6}}[/tex]
need help with homework
Answer:
a
Step-by-step explanation:
when running a half marathon (13.1 miles), it took noah 8 minutes to run from mile marker 1 to mile marker 2, and 19 minutes to run from mile marker 2 to mile marker 4. how long did it take noah to run from mile marker 1 to mile marker 4?
Answer:
27
Step-by-step explanation:
9p³q¹(3p³ - 5q) please help
After simplifying the given expression 9 p³ q¹ ( 3 p³ - 5 q ), we get 27 p⁶ q - 45 p³q².
We are given that:
9p³q¹(3p³ - 5q)
We need to simplify it:
So, we get that:
= ( 9 p³q¹ × 3 p³ ) - ( 9 p³q¹ × 5 q )
Simplify:
= 27 p³⁺³q - 45 p³q¹⁺¹
Simplifying it, we get that:
= 27 p⁶ q - 45 p³q²
Therefore, after simplifying the expression 9 p³q¹ ( 3 p³ - 5q ), we get 27 p⁶ q - 45 p³ q².
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11=2y-11 what is y ?????
hurryy need help fast!!!!!!
Answer:
11=2y-11
11+11=2y
22=2y
y=22/2
y=11
Answer: I got you!
The answer is below!
11=2y-11
11+11=2y
22=2y
y=22/2
y=11
Solve for T
1 < 4 - t
-
Answer:
[tex] \sf \large \: t<3[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
1<4−t
Step 1: Simplify both sides of the inequality.
1<−t+4
Step 2: Flip the equation.
−t+4>1
Step 3: Subtract 4 from both sides.
−t+4−4>1−4
−t>−3
Step 4: Divide both sides by -1.
−t/−1 > −3/−1
t<3
Please help me with my math 60 points
Answer: x=4
HJ=13
JK=5
Step-by-step explanation:
KH=HJ+JK
18=2x+5+3x-7
18=2x+3x+5-7
18=5x-2
5x=20
x=4
HJ=2x+5
HJ=2(4)+5
HJ=8+5
HJ=13
JK=3(4)-7
JK=12-7
JK=5
Please help, answer by tomorrow!!!!
Answer the question in the picture:
Answer:
B
Step-by-step explanation:
its the second one
hope this helps :)
While visiting the zoo, Monika has budgeted $10 for lunch at the café. Can she afford a bacon
cheeseburger, large fries and milkshake? Explain.
The total money Monika spent at the cafe to buy a bacon cheeseburger, large fries and milkshake is $9.9.
Given that, while visiting the zoo, Monika has budgeted $10 for lunch at the café.
How to add decimal numbers?To add decimals, write the numbers in a column, and make sure that the decimal points are aligned. To keep the decimal point in your sum, place a decimal point directly below the decimal points in the addends. Align the decimal point in the sum with the decimal point in the addends, and add a zero if necessary.
Cost of a Cheeseburger= $4.75
Cost of a french fries, a large = $1.90
Cost of a milkshake = $3.25.
Now, the total amount spent at the cafe = Cost of a Cheeseburger + Cost of a french fries, a large + Cost of a milkshake
= (4.75+1.90)+3.25
=6.65 + 3.25
=$9.9
Therefore, the total money Monika spent at the cafe to buy a bacon cheeseburger, large fries and milkshake is $9.9.
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"Your question is incomplete, probably the complete question/missing part is:"
While visiting the zoo, Monika has budgeted $10 for lunch at the café. Can she afford a bacon cheeseburger, large fries and milkshake? Explain.
The cost of food items available at cafe are listed below:
Sandwiches Sides Beverages
Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80
Calculate the interquartile range of the data set below: 30, 6, 1, 22, 19, 7, 8
Answer:
IQR = 13
Step-by-step explanation:
first step is to find the median of the data set.
rearrange the data into ascending order. Then the median is the middle value.
1 , 6 , 7 , 8 , 12 , 19 , 30 ← in ascending order
↑ middle
then median = 8
the interquartile range (IQR) is calculated as
IQR = Q₃ - Q₁ ( Q₃ is the upper quartile and Q₁ the lower quartile )
Q₃ is the middle value of the data to the right of the median
12 , 19 , 30
↑ middle
then Q₃ = 19
Q₁ is the middle value of the data to the left of the median
1 , 6 , 7
↑ middle
then Q₃ = 6
IQR = 19 - 6 = 13
Please help asap. This is for algebra 1
Answer:
A. ≈65in
B. ≈68in
Step-by-step explanation:
Girls: 25 + 1.17h
Boys: 22.7 + 1.37h
A. 25 + 1.17(34) = 25 + 39.78 = 64.78in
B. 22.7 + 1.37(33) = 22.7 + 45.21 = 67.91in
Since it's asking for the nearest inch:
A. ≈65in
B. ≈68in
I hope this helps!
Evaluate the expression
Answer:
16
Step-by-step explanation:
Step 1. Plug the numbers into the equation.
Step 2. Solve using PEMDAS
2 ( 6 + 3 ) - 2
2 ( 9 ) - 2
18 - 2
16