The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.
1) Let's substitute the values into the formula.
S17 = 17/2[2(11) + (17 - 1)6]
S17 = 17/2[22 + (16)6]
S17 = 17/2[22 + 96]
S17 = 17/2[118]
S17 = 17/2 × 118
S17 = 1003
Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003.
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In a circle of music lovers, 14 people play the piano or violin, 8 people are piano players, and
5 people play both instruments. Find the number of violin players.
Answer:
11 people
Step-by-step explanation:
14-8+5
6+5
11
If a kid has to read 11 chapters of a book in eight days how many chapters sould the read each day?
Answer:
About 1 and 1/4 chapters per day.
Step-by-step explanation:
There are 11 chapters, and eight days to read them. So we divide 11 by 8. 11/8 = 1.375, which is approximately 1 and 1/4.
How do you write two and forty seven thousandths in number?
Answer:
47002 :)
is how you write 47 thousand +2
need help asap, will rate 5 stars!!
Answer:
3rd option
Step-by-step explanation:
using the sine and cosine ratios for the 60° angle in the right triangle and the exact values.
cos60° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 12 ( divide both sides by 2 )
x = 6
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
y = 6[tex]\sqrt{3}[/tex]
Using the scale factor you just found, what is the length of the unknown side on the smaller rectangle?
what scale factor did you find and is there a photo of the rectangle?
2 tons of sawdust cost $3,760.00. What is the price per pound?
Answer:
3760/4000(2 tons=4000pounds)
$0.94 is the answer
Put these numbers in order from least to greatest.
13/16
79/80
-10/32
-9
-9, -10/32, 13/16, 79/8]
Step-by-step explanation:
use ur brain
What's equivalent to -8
Answer: try 1 or 0
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
(-8)= 8
Find the coordinate of point C on AB such that the ratio of AC to CB is 3:6
B= (5,6)
A= (-4,-6)
Answer:
Step-by-step explanation:
Solution for Point C is located on AB such that the ratio of AC : CB is 3:2. ... A: Here point B lies on the line AC with coordinates A(-3,4) and C(2,-6), ...
Write an equation of the line through each pair of points in slope-intercept form.
(-1,-4) and (3,-4)
The equation of line is y = -4
Given the points:
(x₁, y₁) = (-1, -4)
(x₂, y₂) = ( 3, -4)
The slope-intercept form:
y = mx + b
Where, m is the slope and b is the y-intercept, that is (0, b)
The formula for slope:
m = (y₂ – y₁) / (x₂ – x₁)
We have given
x₁ = -1
x₂ = 3
y₁ = -4
y₂ = -4
So,
m = (-4 – (-4)) / (3 – (-1)) = (-4 + 4) / (3 + 1) = 0/4 = 0
Therefore we have the equation of the line as:
y = mx + b
-4 = 0(x) + b
-4 = 0 + b
b = -4
Therefore, the equation of line y = -4
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Suppose B is the midpoint of -AC. Use the given information to find the missing measure. A B=4 x-5, B C=11+2 x, A C= ?
Length of AC is 54 units.
The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.
As B is the midpoint of AC,
AB = BC
∴ 4x - 5 = 11 + 2x
∴ 4x - 2x = 11 + 5
∴ 2x = 16
∴ x = 8.
Now, AC = AB + BC
∴ AC = 4x - 5 + 11 + 2x
Substituting the value of x,
∴ AC = 4(8) - 5 + 11 + 2(8)
∴ AC = 54 units
Thus, the length of AC is 54 units.
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please helpppp :3
URGENT
a number y multiplied by 5 is no less than 5/6 An inequality is
Answer:y/5=5/6
Step-by-step explanation:based on given conditons
Evaluate each logarithm.
log₅ 5√5
Answer:
well done...I hope it's helpful
i know its easy but my brain isn't working and my friends aren't answeringngngng
The number of apples in the 12th bag is 9.
How to find the number of apples in the 12th bag using mean number?There are 12 bags of apples on the market stalls.
The mean number of apples in each bag is 8.
Therefore, the number of apples in the 12th bag can be calculated as follows:
mean = ∑fx / ∑f
Hence,
let the number of apples in the 12th bag = a
mean = 6 × 1 + 7 × 4 + 8 × 2 + 9 × 3 + 10 × 1 + x × 1/ 1 + 4 + 2 + 3 + 1 + 1
mean = 6 + 28 + 16 + 27 + 10 + x / 12
mean = 87 + x / 12
8 = 87 + x / 12
cross multiply
96 = 87 + x
x = 96 - 87
x = 9
Hence, the number of apples in the 12th bag is 9.
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Given that R = 4x − 9y Find x when y = 1 and R=1 ?
Answer:
x=2.5
Step-by-step explanation:
R = 4x − 9y
We know that R=1 and y=1 so we can substitute that in
1=4x-9
Then solve as a normal algebraic equation
add 9 to both sides
10=4x
divide both sides by 4
2.5=x
The area of a square is calculated
by squaring the length of one side
of the square.
Margo earns
$13.50 per hour as
earn approximately $300 per week? lifeguard. How many hours per week must she work if she
wants to
Earn approximately $300 per week
Margo works 23 hour per week to earn approximately $300 per week .
The unitary technique could be a technique within which you discover the worth of a unit so the worth of a needed range of units.For simplification, continually write the items to be calculated on the right-hand facet and things best-known on the left-hand facet.It is given that Margo earns $13.50 per hour .
Using unitary method , we get
To get his weekly financial gain, we have a tendency to multiply his hourly wage by the quantity of hours he worked.
Pay = hourly rate × variety of hours worked
300 = 13.50 × number of hours worked
number of hours worked = 300 /13.50
= 22.22
On rounding off , we get the hour = 23 hours
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Write an absolute value inequality and a compound inequality for a length of 8.9mm with a tolerance of 0.15mm
The absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that the length is 8.9 mm with a tolerance of 0.15mm.
The absolute inequality will be written as below:-
x ≥ | 8.9 ± 0.15 |mm
The compound inequality will be written as:-
x > 8.75,
x < 9.05.
Therefore, the absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.
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Determine whether each list is a sequence or a series and finite or infinite. -0.5-0.25-0.125- . . . . . .
The numbers that are given:
-0.5-0.25-0.125- . . . . . .
They are part of an infinite series
What is a series?A series is the summation of a set of numbers or sequences.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
-0.5-0.25-0.125- . . . . . .
If we analyze the variation between each term we have the form:
(-1/2ⁿ)
-1/2¹ = -0.5-1/2² = -0.25-1/2² = -0.125(-1/2ⁿ)
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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Yesterday Philip ate three meals totaling 1600 calories. He ate a total of 750 calories for breakfast and lunch. How many calories did he eat at dinner?
I need this answered please
The man in a video spent 9 minutes and 2 seconds filling his bathtub before taking a bath. After taking the bath, his partner told him that taking a bath was wasting water and that he should shower instead.
Question: How long would he need to run the shower to use the same amount of water as the bath that he took?
Hints:
On the bathtub faucet, it takes 00:00:26:82 seconds to fill a gallon
For the shower head, it takes 00:00:10:84 seconds to fill a gallon
According to the Centers for Disease Control and Prevention (CDC), the average shower lasts 8 minutes. If you like to linger in the shower for longer than 15 minutes, you might want to rethink your hygiene routine.
According to board-certified dermatologist Dr. Edidiong Kaminska, MD, the recommended maximum shower time is about 5 to 10 minutes. This is enough time to cleanse and hydrate the skin without overdoing it. “Our skin needs water, just like our bodies, but if we over- or under-do it, then it may have consequences,” she adds.
And if you have dry skin or eczema, Dr. Anna Guanche, MD, FAAD, says shorter, lukewarm showers are recommended. Moreover, the Baylor College of Medicine says it’s especially important to avoid hot showers in the wintery months since the heat can damage the surface of the skin, which can lead to inflammation and increase symptoms of eczema.
Side effects of long showers
While a long, hot shower might seem like the best way to pamper your body, over-showering may dehydrate the skin. “The purpose of showering is to hydrate and cleanse the skin, but warm or hot showering for prolonged periods strips away natural oils of the skin and opens up our pores and allows moisture to escape,” Kaminska says.
To keep moisture in, she usually recommends applying a body moisturizer after showering to the skin since it allows the water (hydration) to stay in the skin and not escape.
solve for x
3/2 x−4= 1/2 x−3
please help this is so confusing
Answer:
x=1
Step-by-step explanation:
Ok, this is a two step equation, so the first step you will do is get the regular numbers (-4 and -3) on one side of the equation, like this:
3/2x-4=1/2x-3
+4 +4
3/2x=1/2x+1
Next, you need to get the variables on one side of the equation, so you will minus 1/2x like this.
3/2x=1/2x+1
-1/2x -1/2x
2/2x=1
Simplify
x=1
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{3}{2} x-4 = \frac{1}{2} x-3[/tex]
[tex]x - 4 = -3[/tex]
x = 1
What is the value of 6x2 + x if x = 5?
65
35
905
155
Answer:
If it is [tex]6(5)^2[/tex] then the answer is 150
Step-by-step explanation:
So, follow PEMDAS
Parenthesis
Exponent
Multiplication
Division
Addition
Subtraction
First square 5 because there is an exponent [tex]6(5)^2 = 6(25)[/tex]
Next multiply 6 times 25 and you get 150!
Answer:
d) 155
Step-by-step explanation:
The value of x is,
→ x = 5
Now the expression is,
→ 6x² + x
Let's solve the expression,
→ 6x² + x
→ 6(5)² + 5
→ 6(25) + 5
→ 150 + 5
→ 155
Hence, the answer is 155.
I WILL GIVE U MORE BRAINLY POINTS NEED HELP ASAP :d
Answer:
what
Step-by-step explanation:
b. Find the sum of the first ten terms of the Fibonacci sequence. Divide the sum by 11 . What do you notice?
According to the question, the Fibonacci series is a series of sequence of numbers. It follows one standard property which states that every third term in the series is the addition of first term and second term.
Now, the first ten terms of the Fibonacci sequence is as follows:
Fibonacci Series = [tex]{1,1,2,3,5,8,13,21,34,55}[/tex]
The sum of the first ten number of the Fibonacci series is as follows:
Sum = [tex]1+1+2+3+5+8+13+21+34+55 = 143[/tex]
As per question, divide the calculated sum by eleven. Therefore, it can be written as:
Required Division = [tex]\frac{143}{11} = 13[/tex]
Hence, the solution for the given series is [tex]13[/tex].
What is a Fibonacci series?
Fibonacci series is an infinite series of sequences of numbers. The important property of this series is, every third term is the addition of the first and second term. In this, the first term either starts with zero or one.
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use the properties of exponents to write an equivalent expression that is a product of distinct primes, each raised to an integer power.
10 to the 5th power times 9 to the 2nd power over 6 to the 4th power
Answer:
10 to the 5th power times 9 to the 2nd power over 6 to the 4th power
write an equation for the difference of 7 and a number is 18
Rewrite in simplest terms: (−10x+2)+(−9x+8)(-10x+2)+(-9x+8)(−10x+2)+(−9x+8)
The algebraic expression in simplest terms is 200 · x² - 79 · x + 14 = 0.
How to simplify an algebraic expression
In this problem we have a sum of products of binomials as algebraic expression and we must reduce to its simplest terms by using algebra properties, that is, using these properties until a polynomial is found:
(- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)
(- 10 · x + 2) + 2 · (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)
(- 10 · x + 2) · [1 + 2 · (- 10 · x + 2)] + (- 9 · x + 8)
(- 10 · x + 2) · (1 - 20 · x + 4) + (- 9 · x + 8)
(- 10 · x + 2) · (3 - 20 · x) + (- 9 · x + 8)
3 · (- 10 · x + 2) + (- 20 · x) · (- 10 · x + 2) + (- 9 · x + 8)
- 30 · x + 6 + 200 · x² - 40 · x - 9 · x + 8
200 · x² - 79 · x + 14
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