9514 1404 393
Answer:
A. d = ∑[k=1,n] (4.5+0.5k)
B. 9
Step-by-step explanation:
A) The series has first term 5 and common difference 0.5. The general term is given by ...
an = a1 +d(n -1)
an = 5 + 0.5(n -1) . . . . substitute numbers for this series
an = 4.5 +0.5n . . . . . . simplify
The sum is the sum of these terms:
[tex]\displaystyle \boxed{d_n=\sum_{k=1}^n(4.5+0.5k)}[/tex]
__
B) The sum of terms of an arithmetic series is the average of the first and last, multiplied by the number of terms. We want to solve for n to make the sum greater than 60.
[tex]\displaystyle d_n=\frac{n}{2}(5 +4.5 +0.5n)\\\\\dfrac{n}{2}(9.5+0.5n)>60\\\\n(19+n)>240\qquad\text{multiply by 4}\\\\n^2+19n+9.5^2>240+9.5^2\qquad\text{complete the square}\\\\n+9.5>\sqrt{330.25}\qquad\text{square root}\\\\n>18.17-9.5=8.67\qquad\text{positive root, subtract 9.5}[/tex]
Melissa's total distance will first exceed 60 miles the 9th time she trains.
Answer:
A. d = ∑[k=1,n] (4.5+0.5k)
B. 9
Step-by-step explanation:
A) The series has first term 5 and common difference 0.5. The general term is given by ...
an = a1 +d(n -1)
an = 5 + 0.5(n -1) . . . . substitute numbers for this series
an = 4.5 +0.5n . . . . . . simplify
Write the equation of the line in slope-intercept form
Slope= -7/4
Y-intercept= 5
Answer:
y = - [tex]\frac{7}{4}[/tex] x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{7}{4}[/tex] and c = 5 , then
y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line
Find the area of the trapezoid
A. 44 Square units
B. 72 Square units
C. 88 Square units
D. 144 Square units
Answer:
Area = 13+9=22
22/2 = 11
11x 4 = 44 square units
pls answer correctly :)
I literally just did this its B
Find the circumference
Answer:
37.7 cm
Step-by-step explanation:
C = 2πr
diameter = 12cm
radius(r) = diameter ÷ 2radius(r) = 12 ÷ 2radius(r) = 6cmC = 2πr= 2 × 22/7 × 6Circumference = 37.7 cmAntoinette Applied for a $6000 loan, which she will start paying back after the interest has accumulated. She had a initial offer for a simple annual interest rate of 6% for three years, but decided to consider other options. Which of the following options of all the crease the interest she pays the most?
F. $5500 loan, simple interest, annual rate of 6%, term of three years
G. $6000 loan, simple interest, annual rate of 5.75%, term of three years
H. $6000 loan, simple interest, annual rate of 6%, term of 2.8 years
J. $5500 loan, compound interest, annual rate of 6%, term of three years
Please Help
At a glass vase factory, 2 out of the last 20 vases produced were chipped. Considering this data, how many of the next 10 vases would you expect to be chipped?
2 out of 20 = 2/20 which reduces to 1/10 which means 1 out of every 10.
I would expect 1 out of the next 10 to be chipped.
Answer:
1
Step-by-step explanation:
A=144pi^2 ft. Find the radius
A right triangle has an area of 98 square inches. If the triangle is not an Isosceles triangle, what are the all possible lengths of the legs?
Answer:
The possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
Step-by-step explanation:
We are told the above Triangle is not an Isosceles Triangle
Hence, we assume it is a right angle triangle
The area of a triangle is = 1/2 × Base × Height
= let us represent Base and Height = x
Hence:
1/2 × x × x = 98
x² /2 = 98
Cross Multiply
x² = 98 × 2
x² = 196
Step 2
We find the factors of 196
1× 196 = 196 (1, 196)
2 × 98 = 196 (2, 98)
4 ×49 = 196 (4, 49)
7 × 28 = 196 (7, 28)
Therefore, all the possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
Hello! I need a bit of help with this problem.
Answer:
I'm pretty sure it's 15 for orange and 30 for blue
A box contains 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles. 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles. Which color marble is most likely to be picked?
Answer:
A red marble
Step-by-step explanation:
First, add all of the possible combinations of marbles that can be picked from the box ( 2 + 2 + 3 + 5 = 12 ). Next, write down the amount of each marble ( 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles). Then, find the marble that appears most in the box. (red marble). Finally, not only have you found that the red marble is most likely to be picked, you also know the probability of picking a red marble, (5/12).
Answer: red
Step-by-step explanation:
Which of the following is equivalent to
601/2
Answer:
B
Step-by-step explanation:
mixed number: 300 1/2 (reduced or equivalent)
decimal: 300.5 (reduced or equivalent)
percentage: 30,050% (reduced or equivalent)
Give me brainllest
Answer:
300.5 or 300[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Just divide.
find the measure of each angle
Answer:
Step-by-step explanation:
m∠ 1 = 180 - 117
m∠ 1 = 63
m∠2 = the same as m∠ 1
m∠2 = 63
m∠3 is also the same b/c of the same length of the "legs" of the triangle
m∠3 = 63
Need help on this one last question
Answer:
available
Step-by-step explanation:
if its available if available comment
Sarah had 25 candies. Sarah gave 2/5 of the candies to her sister. Of the amount left, she gave 2/3 to her friend. How many candies does Sarah have left for herself?
Answer:
5 candies left for herself
Step-by-step explanation:
please help
if your gonna scam just leave i really need help
Answer:
x = 23
Step-by-step explanation:
The measures of the angles in a triangle add up to equal 180
That being said we can create an equation to solve for x
180 = 2x + 3x + 1 + 3x - 5
Now we solve for x using basic algebra
step 1 combine like terms
2x + 3x + 3x = 8x
1 - 5 = -4
now we have 180 = 8x - 4
step 2 add 4 to each side
-4 + 4 cancels out
180 + 4 = 184
now we have 184 = 8x
step 3 divide each side by 8
8x/8=x
184/8=23
we're left with x = 23
Write the quotient as a mixed number. 99 ÷ 5 = 19 R4
PLEASE HELP :(
Answer:
19 4/5Step-by-step explanation:
99 = 5*19 + 499/5 = 19 + 4/599/5 = 19 4/5Answer:
Solution given
99/5=19 4/5 is your quotient in mixed number.
Girrls and boys plsss i need help like frl:)
D- Most babysit because it pays more per-hour.
The reason this is the correct answer is because the question said which is NOT a valid response. This one is not because it didnt tell you how much they get paid per-hour so its incorrect.
Hope this helps!
Have a great day!
- Hailey
What is the median of the data set? History Test Scores 5 0 8 6 5 6 8 9 7 0 3 5 8 8 0 6 7 7 7 9 0 1 3 5 6 8 9 9 5 0 = 50 points
Answer:
The median is 6
Step-by-step explanation:
I need Help please!!
The ages of six boys are given as 12years 3 months,18years 10months,18years 8months,13years 4months,17years 11month and 15years respectively, what is their average age?
evaluate 5^28·5^-32·5^-4
A. 17,920
B. 0.017920
C. 0.000256
D. 0.00000256
Answer:
D 0.00000256
Step-by-step explanation:
[tex]5^{28} *5^{-32}*5^{-4}=5^{28-32-4}=5^{-8}=\frac{1}{5^{8}} =0.00000256[/tex]
Answer:
B. 0.000256
Step-by-step explanation:
5^28 . 5^- 32 . 5^ -4
= 5^( 28 - 32 - 4 )
= 5^( 28 - 36 )
= 5^- 8
= 1 / 5^8
= 1 / 390625
= 0.000256
PLS ACTUALLY HELP ME , I WILL MARK BRAINLIEST
Answer: 15/8
Step-by-step explanation:
Look at the inequality.
3y > 27
Which set of values for y will make this inequality true?
A. 4,5,8
B. 5, 7,9
C9, 12, 14
D. 11, 13, 22
Answer:
D) 11,13,22
Step-by-step explanation:
If 3y>27, then y>9. Therefore, D is the correct answer (C is not correct BTW because 9 isn't included in the inequality).
Find the perimeter of the figure to the nearest hundredth.
12 in.
5 in.
5 in.
9 in.
perimeter: about
in.
Answer:
50.28 inches
Step-by-step explanation:
From the Image, we can find the length of the arc of the semi-circle by dividing the circumference of the resulting circle by 2
Radius= 9in
C= 2πr
C=2*3.142*9
C=2*3.142*9
C= 56.556 inches
Hence the length of the arc is
=56.556/2
=28.278 inches
The perimeter of the shape
=28.278+5+12+5
=50.28 inches
Answer:
its actualy 50.26, but follow what the guy before me did.
Step-by-step explanation:
One customer paid $12 for 14 postcards and 5 large envelopes. Another customer paid $24.80 for 10 postcards and 15 large envelopes. What was the cost in dollars of each large envelope?
Answer:
$1.42
Step-by-step explanation:
Since, The first customer paid $12 for 14 postcards and 5 large envelopes.
That is, 14 x + 5 y = 12 ------ (1)
And, The second customer paid $24.80 for 10 postcards and 15 large envelopes.
That is, 10 x + 15 y = 24.80 -------(2)
3 × equation (1),
We get, 42 x + 15 y = 36 ---------(3)
Equation (3) - Equation (2)
32 x = 11.20
⇒ x = 11.20/32
⇒ x = 0.35
By putting the value of x in equation (1),
We get, 14 × 0.35 + 5 y = 12
⇒ 4.9 + 5 y = 12
⇒ 5 y = 7.1
⇒ y = 1.42
Thus, the cost of one postcard = $ 0.35
And, the cost of each large envelope = $ 1.42
Help ME DUE in 10 mins WILL GIVE BRAINIEST IF HELP!!! SHOULD BE EASY FOR SOME
Answer:
-9n - 3
Step-by-step explanation:
Angel está adaptando un espacio para hacer actividades recreativas en casa y quiere rodear el borde con plantas, cuántos metros mide el borde si la ecuacion para calcularlo es 2a+2b, donde a representa el ancho y b el largo del espacio, a=1 metro y b=2 metros
Answer:
El borde mide 6 metros.
Step-by-step explanation:
Sabemos que la ecuación para el borde está dada por:
borde = 2*a + 2*b
Si sabemos que:
a = 1 metro
y
b = 2 metros
podemos simplemente remplazar esos valores en la ecuación para el borde, asi obtendremos:
(es decir, donde hay una "a" en la ecuación, escribimos "1 metro", y end donde hay una "b" en la ecuación, escribimos "2 metros", luego resolvemos)
borde = 2*(1 metro) + 2*(2 metros) = 2 metros + 4 metros = 6 metros.
Podemos concluir que el borde mide 6 metros.
Idil has a smart phone data plan that costs $25 per month that includes 10 GB of
data, but will charge an extra $20 per GB over the included amount. How much
would Idil have to pay in a month where she used 4 GB over the limit? How much
would Idil have to pay in a month where she used went over by x GB?
A rectangular garden has an area of 84 square feet and a length of 7 feet. What is the width of the garden?
Answer:
12 ft
Step-by-step explanation:
Given data
Area= 84 ft^2
Length= 7ft
The expression for the area is
Area= L*W
substitute
84=7*W
W= 84/7
W= 12ft
Hence the width is 12 ft
Answer:12ft
Step-by-step explanation:
an athlete did one round around a circle of radius 42m.what is the total distance covered by him
Answer:
2 * pi * 42 meters
Step-by-step explanation:
One round means a parameter of the circle