Based on the calculations on this arithmetic sequence, the value of the first term is equal to -8.
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Given the following data:
Tenth term (a₁₀) = 30.
Common difference = 2.
Substituting the given parameters into the formula, we have;
10 = a₁ + (10 - 1)2
10 = a₁ + (9)2
10 = a₁ + 18
a₁ = 10 - 18
First term, a₁ = -8.
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(2.0 x 10^4)(3.0 x 10^3) = ?
Answer:
6 x 10^7
Step-by-step explanation:
(2x3)(10^4 x 10^3)
6 x 10^4+3
6 x 10^7
4 to the 7th power times 8 to the 7th power?
Answer:
3.435973837*10^10
Step-by-step explanation:
4 to the 7th power is 16384
and 8 to the 7th power is 2097152
multiplied by each other is 3.435973837*10 to the 10th power
if you have to round to the nearest 10th the answer is 3.44
you buy tealight candles and mints as party favors for a babyshower.e tealight candles come in packs of 12 for $3.50. e mints come in packs of 50 for $6.25. whatis the least amount of money you can spend to buy the same number of candles and mints?
The least amount of money you can spend to buy the same number of candles and mints is $125.
The prime factorization of 12 and 15 is:
12= 2*2*3
15= 2*5*5
Now the factor of both appears in both number's factorization so least common multiple is:
LCM of 12 and 15 = 2*2*3*5*5=300
It is given that candies come in packs of 12 and mints in packs of 50.
Hence, the total quantity of packs of each thing is:
Candles: 300÷12=25
Mints: 300÷50=6
The least amount of money to be spent is:
25×$3.50 + 6×$6.25= $87.5 + $37.5= $125
Thus, the least amount of money you can spend to buy the same number of candles and mints is $125.
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Answer:125
Step-by-step explanation: no explanations sorry but it is right thank me later
PLSSSSSS ANSWERRRRRRRRRRR
What is the difference between the area of the square and the area of the circle?
The difference between the area of the square and the area of the circle is C. 9x²(4 - π).
How to calculate the area?The area of the square will be:
= Side ×Side
= 6x × 6x
= 36x²
The area of the circle will be:
= πr²
= 3.14 × (3x)²
= π × 9x²
= 9πx²
The difference will be:
= 36x² - 9πx²
= 9x²(4 - π)
Therefore, the correct option is C.
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The difference between the area of the square and the area of the circle is 9x²(4 - π)
How to find the difference of the area of circle and a square?area of circle = πr²
where
r = radiusTherefore,
area of a square = l²
where
l = side lengthThe circle is inscribed in the square.
Therefore, the difference in area of the square and circle is as follows:
area of circle = π × (3x)² = 9x²π
area of the square = (6x)² = 36x²
Hence,
difference in area = 36x² - 9x²π
difference in area = 9x²(4 - π)
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The perimeter of a square is four times as great as the length of any of the sides determine if the perimeter of a square is proportional to the sides of its length explain
The perimeter of a square is proportional to the sides of its length
How to determine if the perimeter of a square is proportional to the sides of its length?The statement is given as
The perimeter of a square is four times as great as the length of any of the sides
The above statement can be represented as
P = 4L
Where P represents the perimeter and L represents the side length
A proportional equation is represented as
y = kx
Where k a constant
By comparing y = kx and P = 4L, we have
y = P, k = 4 and x = L
Hence, the perimeter of a square is proportional to the sides of its length
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The constants a, c and d are positive. Solve the inequality for x.
d-cx>a
The solution to the give inequality is x < d-a/c
Solving inequalitiesAn inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given the inequality expression
d - cx < a
Make x the subject of formula to have:
-cx < a - d
Divide both sides by -c
-cx <(a-d)/-c
x < -(a-d)/c
x < d-a/c
Hence the solution to the give inequality is x < d-a/c
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calculate the length in m of a right triangle's hypotenuse when the other two sides measure 2 m and 4m respectively.
The length of hypotenuse is 4.5 meters.
The length of hypotenuse can be calculated using Pythagoras theorem. Writing the Pythagoras theorem below -
Hypotenuse² = Base² + Perpendicular²
The given other two sides will be base and perpendicular. So, keeping the values in mentioned equation of Pythagoras theorem to find the value of Hypotenuse.
Hypotenuse² = 2² + 4²
Taking square of the numbers to find the value of Hypotenuse
Hypotenuse² = 4 + 16
Performing addition to find the value of Hypotenuse
Hypotenuse² = 20
Hypotenuse = [tex]\sqrt{20}[/tex]
Taking square root to find the value of Hypotenuse
Hypotenuse = 4.5 meters
Hence, the length in meters of a right triangle's hypotenuse is 4.5 meters
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Theoretically, If the spinner is spun 400 times, how many times would you expect to get blue?
Based on the experiment, if the spinner is spun 400 time, how many times would you expect to get blue.
The number of times that blue will be expected will be 100 times.
What will be the probability of getting a blue?It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.
It simply means that each color has a 1/4 chance for each scenario.
Therefore, the number of times that blue will be expected will be:
= 1/4 × 400
= 100 times
Therefore, the number of times that blue will be expected will be 100 times.
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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?
a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.
The percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.
What is normal distribution?The normal distribution, also recognized as that of the Gaussian distribution, would be a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far away from the mean. The normal distribution is represented graphically as a "bell curve."
Now, according to the question;
The formula for finding the z-score is;
z = (x - μ)/σ
where,
x is the score
μ is the mean
σ is the standard deviation.
Summer vacation costs $1,755 for the average local family.
The distribution is normal, with a standard deviation of $390.
We need to figure out what percentage of families took vacations less than $1200.
The mean is $1,755
∴ μ = $1,755
∵ The standard deviation is $390
∴ σ = 390
∵ The vacation cost is under $1200
∴ x = $1200
Substitute the values in the formula of z score.
z-score = (1200 - 1,755)/390 = -1.42
Use the negative normal distribution table of z
P(z < 1,200) = 0.07782
P(x < 1,200) = P(z < 1,200)
P(x < 1,200) = 0.07782
P(x < 1,200) = 7.78%
Therefore, the percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.
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The complete question is -
International travel is usually more expensive than domestic travel. A recent survey found that the average per-person cost of a 12-day international vacation is $1,755. This includes transportation, food, lodging, and entertainment.
a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.
Tanner is going to play at an arcade. There is a $4.50 admission fee, and each game costs $0.75 to play. If Tanner only brought $20.00 to spend, what is the maximum number of games that he can afford to play?
Answer:
[tex]12 > x[/tex]
Step-by-step explanation:
[tex]20 > .75x + 4[/tex]
Is the equation you need to set up.
Then you want to subtract four from both sides ehich ends up giving you
[tex]16 > .75x[/tex]
Then divide 16 by 4 (this gives you a fourth) you get four
Then multiple 4 by 3 to get .75 of 16 which is 12
Hope this helps!
If yoy have any other questions feel free to ask!
Answer:
Tanner can play 20 games in the arcade and will have 50 cents left over.
Step-by-step explanation:
20 = 4.50 + 0.75x
Subtract 4.5 from both sides.
15.5 = 0.75x
Plug in numbers for x until it is equal more that 15.5
x = 20
0.75(20) = 15
0.75(21) = 15.75 < too much
24 ÷ (−6) =
−15 ÷ 0.3 =
−4 ÷ (−20) =
pls hlp :< i feel rly nauseous
Answer:
1st Question 24 ÷ (-6) = -4
2nd Question -15 ÷ 0.3 = -50
3rd Question -4 ÷ (-20) = 0.2
This should be correct. I used a calculator Lol. :3.
ruben made a scale drawing of a petting zoo. the scale of the drawing was 1 millimeter : 10 meters. if the actual length of the goat pen is 20 meters, how long is the pen in the drawing?
The length of the pen in the drawing will be 2 millimeters.
As we can't create a real-life dimension in a small sheet of paper, we opted for a small scale that covers up the large length.As we are given, the scale of the drawing is 1 millimeter: 10 meters, which is 1 millimeter for every 10 meters
As we have been given that the actual size of the goat pen is 20 meters, so the length of the pen in the drawing is = 20*(1/10)
= 2 millimeters
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'
The length and breadth of a land are x m and y m respectively . If perimeter of the land is 420 m, then
a. Write the equation which represent perimeter of land
b. If length of the land is 120 m, then find the breadth
Answer:
90 m
Step-by-step explanation:
a. Perimeter = 2( length + breadth) 2(x + y)
Answer: Perimeter: 2(x + y) = 420
or 2x + 2y = 420
Using the values given
b.
2x + 2y = 420 (perimeter p= 420)
2(120) + 2y = 420 (length x = 120)
240 + 2y = 420
2y = 420 - 240 = 180 (subtract 240 on both sides)
y = 190/2 = 90 m
Members of a softball team raised $2045.50 to go to a tournament. They rented a bus
for $1041.50 and budgeted $62.75 per player for meals. Which equation or tape
diagram could be used to represent the context if p represents the number of players
the team can bring to the tournament?
The equation used to represent the context is 1041.50 + 62.75p = 2045.50.
How to compute the equation?From the information, they rented a bus for $1041.50 and budgeted $62.75 per player for meals.
Therefore, the equation will be:
1041.50 + (62.75 × p) = 2045.50
1041.50 + 62.75p = 2045.50
Therefore, the equation will be 1041.50 + 62.75p = 2045.50.
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3 2/5 + -7 1/5.
Please hurry I am desperate!
Answer:
-3.4 or -17/5
Step-by-step explanation:
3 and 2/5= 17/5 or 3.4
-7 and 1/5 = -34/5 or -6.8
Gary, the school chef, needs to make 40 tacos for every 15 students. How many tacos would Gary need to prepare for 3 students?
Answer: 8 tacos
Step-by-step explanation: To turn 15 into 3 students you would divide 15 by 5. You would also have to divide 40 by 5 too so that would be 8 tacos.
The width rectangle is three less than twice its length. If the area of the rectangle is 193 cm² what is the length of the diagonal?
Answer:
Step-by-step explanation:
Givens
Let the Length = L
Let the width = w
w = 2*L - 3
Area = L * w
Area = 193
Solution
Area = 193
193 = L*(2L - 3)
193 = 2L^2 - 3L Subtract 193 from both sides.
2L^2 - 3L - 193 = 0
You have to use the quadratic formula get the answer. Without going through all all that, I will tell you that the only value you can use for L is 10.6
L = 10.6
w = 2* 10.6 - 3 = 18.4
But you want the diagonal. Use the Pythagorean Theorem to get it.
Diagonal^2 = L^2 + w^2
Diangonal^2 = 10.6^2 + 18.4^2
Diagonal^2 = 450.92 Take the square root of both sides
√diagonal^2 = √450.92
Answer
The diagonal is 21,23
FIRST PERSON TO ANSWER WILL GET BRAINLEST
What will be the location of the y value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( -17, -3)
Using translation concepts, the y-coordinate of R' will be of -10.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the rule is given by:
(x,y) -> (x + 4, y - 7)
y -> y - 7 means that for the image, the 7 is subtracted from the y-coordinate of the pre-image. The y-coordinate of R is of -3, -3 -7 = -10, hence the y-coordinate of R' will be of -10.
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PLEASEEEEEE HELP ASAP
WILL GIVE BRAINLIST!!
DONT JUST USE FOR POINTS, ACTUALLY ANSWER IT! (CORRECTLY)
THIS IS FOR IXL BTW
Answer:
96
Step-by-step explanation:
It is a straight linek so it adds up to 189.
53+31 = 84
180-84=96
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arrange the following fractions in ascending order: 3/13, 1/4, 1/7
3/13 least
1/7
1/4 greatest
Write an equation for a line parallel to y=4x+5 and passing through the point (4,13)
CAN SOMEONE HELP PLEASE IM CONSTANTLY GETTING IGNORED.
Answer:
7GB, $12
Step-by-step explanation:
I used subtraction to find the difference.
|2b – 3y| + 5z if b = −3, y = −4, and z = −1
a hospital day staff consists of 25 registered nurses, 75 unlicensed assistants, five phlebologists, six receptionists and office staff, and 45 physicians. one summer day the staff was at only 68% strength. how many people were working that day? (enter numeric value only. if rounding is necessary, round to the nearest whole number.
The number of people working on that day are 107 people in the staff.
According to the statement
We have to find that the number of people were working that day.
So, For this purpose, we know that the
A percentage is a number or ratio expressed as a fraction of 100.
From the given information:
a hospital day staff consists of 25 registered nurses, 75 unlicensed assistants, five phlebologists, six receptionists and office staff, and 45 physicians. one summer day the staff was at only 68% strength.
Then
Total number of staff = 25+75+5+6+45
Total number of staff = 156
Then
the staff was at strength = 68%
And then
Number of people working on that day = 68% of 156
And
Number of people working on that day = 68/100 *156
Number of people working on that day = 0.68*156
Number of people working on that day = 106.08
Approximate 107 people.
So, The number of people working on that day are 107 people in the staff.
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find the value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1?
The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.
Expression
An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.
Given that:-
Expression : 5x -2y + 3z
x = 7, y = 11 , z = -1
We have to find the value of 5x - 2y + 3z
According to the data given in the question, we can write,
The value of the expression 5x - 2y + 3z is:-
5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.
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Convertir o.83333 = 0.83 a fracción común
Answer:
83/100
Step-by-step explanation:
You move 2 times to the right your answer will be 83/100
(1’^0)^1 d) (1v0’)^(0v1) Logic statements
We need to know about logic statements to solve this problem. The solution of the logic statements are 0 and 1 respectively.
Logical operators are used to form logical statements, logical operators compute result based on boolean values true and false or binary 1 and 0. The common logical operators are AND and OR. AND is represented by ^ symbol and OR is represented by v symbol, ' means negation of the value, which means that true becomes false and vice versa. For AND operator, it works like multiplication, 0 and 1 yield 0, 1 and 1 yields 1 and 0 and 0 yields 0. For OR operator it works like addition, 0 and 1 yields 1, 1 and 1 yields 1 and 0 and 0 yields 0. For the logical statements given in the question we need to first compute the logical statement inside the bracket and then compare the inner result with the outer value.
(1'^0)^1 =(0^0)^1=0^1=0
(1v0')^(0v1)=(1v1)^(0v1)=1^1=1
Therefore we found the values of the logical statements to be 0 and 1 respectively.
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Jack purchased 3 yards of material to make a coat. He used
5
-
8 yard. How many yards of material does Jack have left?
Jack has left with the 19/8 yards fraction part of material.
What is Yards?In mathematics, yard is the unit of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:
In inches :1 yard = 36 inches
In feet :1 yard = 3 feets
In meters :1 yard = 0.914 meters
For the question given,
If we have to find the remaining material that has been left we must find the difference between the two i.e. used and purchased material by simply subtracting them.
So, Material purchased = 3 yards
Material used = 5/8 yards
now, material left = Material purchased - material used
= 3 - 5/8
= 19/8 yards
Thus, Jack has left with the 19/8 yards material.
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ian and his brother are driving from city a to city b. the two cities are 294 miles apart. ian drives 49 miles per hour. how long does it take them to make the trip?
Answer: 6 hours
Step-by-step explanation: The distance is 294 miles. The speed is 49 miles per hour. In that case, we divide 294 by 49, which gives us 6.