Answer:
The equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
[tex]a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13[/tex]
So, the common difference d is 13
Now, equation for nth term will be:
[tex]a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2[/tex]
So, the equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
where n=1,2,3..
jacks cow is tied to a beanstalk with a piece of rope that is 15ft long. what is the exact area of the circle in which a cow can graze?
Answer:
705.5 ft^2
Step-by-step explanation:
a=πr²
a=π15²
a=π225
a=(3.14)(225)
a=705.5
If pencils sell at 6 for 59¢, how many pencils can be bought for $2.95?
30
First you divide 2.95 by .59, which is 5.
Then you multiply 6 by 5, and get 30!
Devon is five years younger than Sydney the sum of their ages is 57 what is Sydney
Answer:
Sydney is 31 years old.
Step-by-step explanation:
LET age of Devon be x years
and let age of Sydney be y years
if x=y-5-------(i)
x+y= 57 (sum)
Using (i)
(y-5)+y=57
2y=62
y=31
What is the tangent ratio for D
The number of leaves that fall off a tree n days after day 1 is given by the function f (n) = 3(2)".
What does the value 3 mean in this function
Answer:
the amount of leaves that fall of the tree in one day
Step-by-step explanation:
n is the amount of days
f is the amount of leaves that fall in a day
Which situation cannot be represented by the equation x + 10 = 45?
A Marissa spent $45 on a hat and a shirt. The hat cost $10. What is x, the cost of the shirt in
dollars?
B Nicholas rode his bike 45 miles last week. He rode 10 miles on Tuesday and the rest of the
miles on Wednesday. What is x, the number of miles Nicholas rode his bike on
Wednesday?
C Two players scored a total of 45 points in a game. One player scored 10 points. What is x,
the number of points scored by the other player?
D There are 45 students in a group. There are also 10 adults in the group. What is x, the
total number of students and adults in the group?
Answer: D
because the other options actually make sense ;)
Answer:
D
Step-by-step explanation:
the equation of function is y=4x+5 what is the value of y when x=3?
Answer:
y=17
Step-by-step explanation:
y=4x+5
change x to 3
y=4(3)+5
y=12+5
y=17
The required value of y is 17 when x=3 for the given equation y = 4x + 5.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The equation of function is given in the question, as follows:
y = 4x + 5
We have to determine the value of y when x=3 for the above equation.
As per the question, we have
y = 4x + 5
Substitute the value of x = 3 in the above equation,
y = 4(3) + 5
y = 12 + 5
y = 17
Thus, the required value of y is 17.
Learn more about the equations here:
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#6* #6 Multiples Σ > Which answer choice has ONLY multiples of a. 7, 14, 21, 35, 56 b. 7, 21, 27, 35, 49 c. 7, 14, 28, 43, 56 d. 7, 21, 28, 49, 53
Answer:
A
Step-by-step explanation:
B) No 27 is a multiple of 3 alone.
C) No 43 is prime. If you replaced it with 42 all would be well.
D) N 53 is prime.
A) everything is divisible by 7.
PLS HELP GIVING 25 POINTS PLS PLS
Answer A is 28
Step-by-step explanation:
Answer:
oop
Step-by-step explanation:
Express square root of 169^5 using rational exponents
Answer:
The square root is 371293.
Step-by-step explanation:
We solve this question using properties of exponents.
The square root of 169 is 13, so the exponent given can be written as:
[tex]169^{5} = (13^{2})^5 = 13^{10}[/tex]
The square root of [tex]13^{10}[/tex] is given by:
[tex]\sqrt{13^{10}} = 13^{\frac{10}{2}} = 13^5 = 371293[/tex]
The square root is 371293.
Find the slope and the y-intercept of the line.
5x-2y = -4
Write your answers in simplest form.
slope:
Undefined
X
y-intercept: |
?
Answer:
Slope 'm' = [tex]\frac{5}{2}[/tex]
And y-intercept = 2
Step-by-step explanation:
Slope-intercept form of a line is given by the equation,
y = mx + b --------(1)
Here, m = slope of the line
b = y-intercept
Given equation is,
5x - 2y = -4
2y = 5x + 4
y = [tex]\frac{5}{2}x+2[/tex]
By comparing this equation with equation (1),
Slope 'm' = [tex]\frac{5}{2}[/tex]
And y-intercept = 2
A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:
769 691 699 730 711 765 702 718 719 712 768 688 757
695 768 735 709 758 708 693 736 700 687 772 715
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)
Answer:
A.
mean = 724.2
Median = 715
Mode = 768
B.
Range = 85
Standard deviation = 29.30
C.
Interval = [665.6, 782.8]
Step-by-step explanation:
Number of samples n = 25
Summation X= 769 + 691 + 699 +730+711+ 765+ 702 718 +719 +712+ 768 +688 +757+695 768 +735 +709 +758 +708+ 693 +736 700+ 687 +772 +715 = 18105
A.
1. Mean = 18105/25
= 724.2
2. Median is the middle value when arranged from the least value to the highest = 715
3. Mode is the number with the highest frequency = 768 (occured two times)
B.
1. Range = highest value - lowest value
Highest value = 772
Lowest value = 687
772-687 = 85
2. Standard deviation = √(X-barX)²/n-1
= √20604/25-1
=√858.5
= 29.30
Please check attachment for the full calculation of the standard deviation
C.
Interval
[Mean - 2(sd), mean + 2(sd)]
= [724.2-2x29.3, 724.2+2x29.3]
=[665.6, 782.8]
There are three types of sweet in a jar and this table gives
some information about them.
Type of sweet Eclair Humbug Mint
Number of sweets (see picture 4 3x + 6 2x)
A sweet is chosen at random.
The probability it is an eclair is
15
Work out the probability it is a humbug.
Answer:
Answer:
2/3
Step-by-step explanation:
Given:
Number of eclairs = 3
Number of humbugs =2x+6=2(x+3)
Number of mints = x
Therefore, total number of sweets in the jar is,
s=3+2x+6+x=3x+9=3(x+3)
Now, probability of selecting a sweet to be humbug is given as:
p(humbug)= number of humbugs/number of sweets
p(humbug)=2(x+3)/3(x+3)=2/3
Therefore, the probability that it is a humbug is 2/3
Step-by-step explanation:
Solve by elimination
5x+6y= -10
3x-2y= -6
[tex]x = - \frac{2(5 + 3y)}{5} [/tex]
Solving for Y.[tex]y = - \frac{5(2 + x)}{6} [/tex]
Second equation:Solving for X.[tex]x = \frac{2(y - 3)}{3} [/tex]
Solving for Y.[tex]y = \frac{3(2 + x)}{2} [/tex]
Plz help brainlest if correct
Answer:
Help with what....????
Step-by-step explanation:
Find the distance between the points (3,5) and (12,2).
?
Answer:
9.48
Step-by-step explanation:
Answer:
3√10 or about 9.49 units.
Step-by-step explanation:
To find the distance between any two points, we may use the distance formula given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let (3, 5) be (x₁, y₁) and (12, 2) be (x₂. y₂). By substitution:
[tex]d=\sqrt{(12-3)^2+(2-5)^2[/tex]
Evaluate:
[tex]d=\sqrt{(9^2)+(-3)^2[/tex]
Square:
[tex]d=\sqrt{81+9}[/tex]
Simplify:
[tex]d=\sqrt{90}=\sqrt{9\cdot10}=\sqrt{9}\cdot\sqrt{10}=3\sqrt{10}\approx9.49[/tex]
The distance between (3, 5) an (12, 2) is 3√10 or about 9.49 units.
The function of f is defined as follows
Answer:
f(-121) = -5
f(31) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = ∛(x - 4)
f(-121) is x = -121
f(31) is x = 31
Step 2: Evaluate
f(-121)
Substitute in x: f(-121) = ∛(-121 - 4)[Radical] Subtract: f(-121) = ∛(-125)[Radical] Evaluate: f(-121) = -5f(31)
Substitute in x: f(31) = ∛(31 - 4)[Radical] Subtract: f(31) = ∛27[Radical] Evaluate: f(31) = 34 Alz(CO3)3
Do u multiple the 4 with the stuff in the parentheses ?
Answer:
a total of 56 atoms
Step-by-step explanation:
Aluminum carbonate is the compound
Yes, you multiply what is inside the parentheses times 4 and also times 3. That is:
8 atoms of Al
36 atoms of Oxygen
and
12 atoms of Carbon
giving a total of 56 atoms
A population has a standard elevation of 25.29 what is the approximate standard error of the mean for a sample size of 175
Answer:
D. 1.91
(got it right on edmentum)
for your assurance please look at the picture below↓Step-by-step explanation:
The standard error is 1.91.
How is Standard Error Calculated ?For a data set the standard error is calculated by the ratio of standard deviation and square root of the sample size.
[tex]\rm Standard \; Error= \dfrac{ \sigma}{\sqrt{n}}[/tex]
Substituting the values
Standard Deviation = 25.29
Sample size = 175
Standard Error = 25.29 / √175
Standard Error = 1.91
Therefore the standard error is 1.91.
To know more about Standard Error
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Aubrey buys 2 souvenirs during each day of vacation. Write an equation that shows the relationship between the days of vacation x and the number of souvenirs bought y.
Write your answer as an equation with y first, followed by an equals sign.
Answer:
2X = Y
Step-by-step explanation:
To determine the equation that will allow to establish the amount of souvenirs bought by Aubrey (Y), taking into account that for each day of vacation (X) buys 2 souvenirs, the following must be taken into account:
The number of days (X) must be multiplied by 2. Thus, if you buy 2 souvenirs per day and your vacation lasts 4 days, you will have bought 8 souvenirs (4 x 2). Thus, the value of Y is equal to 2X, that is:
2X = Y
[tex]3/5 of 5/9\\[/tex]
Answer:
⅓
Step-by-step explanation:[tex] \frac{5}{9} \times \frac{3}{5} [/tex]
[tex] = \frac{1}{3} \times \frac{1}{1} [/tex]
[tex] = \frac{1}{3} [/tex]
Checking:[tex] \frac{1}{3} \div \frac{3}{5} [/tex]
[tex] = \frac{1}{3} \times \frac{5}{3} [/tex]
[tex] = \frac{5}{9} [/tex]
#CarryOnLearning
Hey there!
When you see the word “of” in mathematical statement, it usually means “multiply” (aka Multiplication)
“3/5 of 5/9”
3/5 • 5/9
MULTIPLY the NUMERATORS (TOP NUMBERS) from each other & also MULTIPLY the DENOMINATORS (BOTTOM NUMBERS) from each other!
3(5) / 5(9)
3(5) = 15 ⬅️ NUMERATOR
5(9) = 45 ⬅️ DENOMINATOR
15/45
The GCF (Greatest Common Factor) for both of your numbers is: 15.. so DIVIDE both the NUMERATOR and DENOMINATOR from 15
15 ÷ 15 / 45 ÷ 15
15 ÷ 15 = 1 ⬅️ NUMERATOR
45 ÷ 15 = 3 ⬅️ DENOMINATOR
Answer: 1/3 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
hey guys i need help plz will give brainlist
Step-by-step explanation:
Effective resistance in the 30Ω and 40Ω parallel circuit = 1 / (1/30 + 1/40) = 120/7 Ω.
20Ω + 10Ω = 30Ω
Effective resistance in the 50Ω and (20Ω + 10Ω) parallel circuit = 1 / (1/50 + 1/30) = 75/4 Ω.
Now we can add the resistances up:
Effective resistance for circuit
= 120/7 Ω + 75/4 Ω = 1005/28 Ω.
Hence I = V / R
= 9.0V / (1005/28 Ω) = 0.25A. (2s.f.)
I need help with these two questions ASAP thank you.
Answer:
There isn't a clear answer
Step-by-step explanation:
4. (LT 1.1) The perimeter of the rectangle below is 40 feet. Its length and width are
given in terms of x. Find the length and width of the rectangle.
3x
2x + 5
Answer:
Length, L = 9 feet.
Width, W = 11 feet.
Step-by-step explanation:
Given the following data;
Perimeter = 40 feet
Length = 3x
Width = 2x + 5
The perimeter of a rectangle is given by the formula;
P = 2(L + W)
40 = 2(3x + 2x +5)
40 = 2(5x + 5)
40 = 10x + 10
10x = 40 - 10
10x = 30
x = 30/10
x = 3
Now, to find the length;
Length, L = 3x
Substituting into the equation, we have;
Length, L = 3*3
Length, L = 9 feet
To find the width;
Width, W = 2x + 5
Substituting into the equation, we have;
Width, W = 2(3) + 5
Width = 6 + 5
Width, W = 11 feet.
I WILL GIVE BRAINLIEST PLZ ANSWER DUE IN A FEW MINUTES
What is every factor of 116
Answer:
1,2,4,29,58,116
Step-by-step explanation:
Prime factorization 116=2x2x29
The number of books that Jordan has read is greater than 22.
HELP PLSS
Answer:
x>22
Step-by-step explanation:
simplify the expression 9(h - 1)
Answer:
9h - 9
Step-by-step explanation:
9(h - 1)
distribute
(9 * h) + (9 * - 1)
9h + (9 * - 1)
9h + -9
9h - 9
Answer:9h-9
Step-by-step explanation:
please help due in 10 mins!!
Answer:
Step-by-step explanation:
C
trops have 3 eyes
Bops have 2 eyes
there are 31 eyes altogether
haw many trops were there ?
how many bops were there ?
Answer:
3 trops
11 bops
Step-by-step explanation:
3×3=9
11×2=22
22+9=31
Please help!!
a. What is the x intercept of the line graphed above?
b. What is the Y intercept of the line?
c. What is the slope of the line?