What is the sum of the series (image below)
a. 1,830
b. 2,010
c. 5,400
d. 5,490
Answers
Answer:
d. 5490
Step-by-step explanation:
[tex]\begin{aligned}\displaystyle \sf \sum_{n=1}^{60} 3n & =3(1)+3(2)+3(3)+...+3(49)+3(50)\\ & = 3+6+9+...+147+150\end{aligned}[/tex]
Therefore, this is an arithmetic series with:
first term (a) = 3common difference (d) = 3Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]
Therefore, the sum of the first 60 terms:
[tex]\begin{aligned}S_{60} &=\dfrac12(60)[2(3)+(60-1)3]\\ & =30[6+(59)3]\\ & = 30[6+177]\\ & = 30[183]\\ & = 5490 \end{aligned}[/tex]
Answer:
The answer is D) 5,490.
Step-by-step explanation:
Related Questions
Which of the following numbers are greater than or equal to 1.75?
Choose all answers
A) 1 4/11
B) 1.6
C) 7/4
Answers
Answer:
Only C
Step-by-step explanation:
1 4/11 is 1+4/11 and 4/11 is less than 1/2 so it has to be less than 1.5, which is less than 1.75
1.6 is less than 1.75 because 1.75-1.6 is 0.15 which is a positive number
4/7 is 1 3/4 which is 1.75
Answer:
a and c
Step-by-step explanation:
they are over 1
In how many ways can she grab 3 Snickers, 2 Starbursts, and 2 Reese's?
Answers
(1) Basket (2) Hands (3) Cart. 3 ways i can think of
Why is this a right triangle? A) Two angles are acute. B) One angle measures exactly 90°. C) All three angles are less than 90°. D) All three sides are of equal length.
Answers
Answer:
B)
Step-by-step explanation:
The main feature in a right triangle is that it has a right angle (90°)
Hope this helps
Queetlon 10 or 15
People leaving the library were aaked how many books they checked out that
day The resulta are:
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Which histogram correctly ahows the data set?
Books Checked Out
0-5 6-11 12-1718-23
Number of booke
Books Checked Out
Answers
Answer:
[B]
Step-by-step explanation:
Given:
People leaving the library were asked how many books they checked out that day The result are: 1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
To Find:
Which histogram correctly shows the data set?
Solution:
Since it given from the histogram:
0-5, 6-11, 12 - 17,18-23
From the result :
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Thus,
1,2,3,5 = 0-5
8,9,10,11 = 6-11
12,13,14,15,16 = 12-17
18,20 = 18-23
From this we can see that:
for
0 - 5 = 4
6 - 11 = 4
12 - 17 = 5
18 - 23 = 2
Hence, the answer is [B]
Kavinsky
pls help complete the sequence
Answers
Step-by-step explanation:
1,2,4,8,16,32,64,128
Multiplying by 2
1,3,5,7,9,11
Adding 2
30, 25, 20, 15, 10, 5
Subtracting 5
Answer:
1,2,3"8"16,32"64"128
1"3"5,7"9"11
30"25""20"15,10,5
Step-by-step explanation:
by x2
The cost, y, of red apples can be represented by the equation y = 2x, where x
is the number of pounds of red apples.
The graph shows the cost of green apples.
Which type of apple costs more per pound?
Cost of Green Apples
11
10
PLEASE HURRY I NEED IT IN 5 mins
Cost (5)
.
3
Weight (pounds)
A. Red apples
B. Red and green apples cost the same.
C. Green apples
Answers
Answer:
red apples
Step-by-step explanation:
1 lb of green apples is 1.5
1 lb of red apples is 2
what are the steps to solving 7(x+2)=91
X=11
Answers
Answer:
Below.
Step-by-step explanation:
7(x + 2) = 91
Distribute the 7 over the parentheses:
7x + 14 = 91
Subtract 14 from both sides of the equation:
7x = 91 - 14
7x = 77
x = 77/7 = 11.
Answer:
X=11
Step-by-step explanation:
[tex]7\left(x+2\right)=91[/tex]
Divide both sides by 7:
[tex]\frac{7\left(x+2\right)}{7}=\frac{91}{7}[/tex]
Simplify:
[tex]x+2=13[/tex]
Subtract 2 from both sides:
[tex]x+2-2=13-2[/tex]
Simplify:
X=11
If f(1) = 1 and f(n) = 5f(n-1) + 4 then find the value of f(5).
Answers
Answer:
[tex]f(5)=1249[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=1[/tex][tex]f(n) = 5f(n-1)+4[/tex][tex]\implies f(2) = 5f(1)+4=5(1)+4=9[/tex]
[tex]\implies f(3) = 5f(2)+4=5(9)+4=49[/tex]
[tex]\implies f(4) = 5f(3)+4=5(49)+4=249[/tex]
[tex]\implies f(5) = 5f(4)+4=5(249)+4=1249[/tex]
Please help me - geometry
Answers
Answer:
v≈4.7
w≈1.6
Step-by-step explanation:
sin71º＝v/5
v=5*sin71º≈4.7
cos71º＝w/5
w=5*cos71º≈1.6
pls help me solve this answer its urgent
Answers
Answer:The equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
Step-by-step explanation:Lines that are perpendicular to each other have slopes that are negative reciprocal of each other.
For example, if a line has a slope of 2, the slope of a line that is perpendicular to it would be, -1/2 (negative reciprocal of 2).
Determine the slope of the given line whose equation is, y + 2 = 3/2(x + 4). Rewrite the equation in slope-intercept form [y = mx + b]:
y + 2 = 3/2x + 6
y = 3/2x + 6 - 2
y = 3/2x + 4
The slope is therefore 3/2.
Negative reciprocal of 3/2 is -2/3.
Examine each of the equations given and see which equation has a slope of -2/3.
A. y = -3/2x +4, the slope is -3/2.
B. y = -2/3x + 4, the slope is -2/3. (perpendicular)
C. y = 2/3x +4, the slope is 2/3.
D. y = 3/2x +4, the slope is 3/2.
E. y+1=-4/6(x+5), rewrite in slope-intercept form
y+1=-4/6x + 20/6
y + 1 = -2/3x + 10/3
The slope is -2/3. (perpendicular)
F. y+ 1 = 3/2(x + 5), the slope is 3/2.
Therefore, the equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
If a1 = 7 and an = an-1 + 4 then find the value of a4.
Answers
Answer:
[tex]a_4=19[/tex]
Step-by-step explanation:
Given:
[tex]a_1=7[/tex][tex]a_n=a_{n-1}+4[/tex][tex]\implies a_2=a_{1}+4=7+4=11[/tex]
[tex]\implies a_3=a_{2}+4=11+4=15[/tex]
[tex]\implies a_4=a_{3}+4=15+4=19[/tex]
Put values get answer
a_n=a_(n-1)+4a_4=a_3+4a_4=a_2+4+4a_4=a_1+4+4+4a_4=7+12a_4=19Which polynomial matches the expression -x (x – 3)?
Answers
Answer:
=> -x² + 3x
Step-by-step explanation:
-x (x – 3)
=> -x² + 3x
Harper has a bag that contains apple chews, cherry chews, and lime chews. She
performs an experiment. Harper randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Harper performs the experiment 38 times.
The results are shown below:
An apple chew was selected 22 times.
A cherry chew was
selected 6 times.
A lime chew was selected 10 times.
Based on these results, express the probability that the next chew Harper removes
from the bag will be lime chew as a percent to the nearest whole number.
Answers
The question says that out of the 38 chews taken out of the bag, 10 of them were lime chews. All we need to do to answer this question is to put that into a percentage. We can do this by doing 10/38 and then multiplying by 100. This will give 26.32%. Since we want this to the nearest whole number we will round to 26%.
Hope this helps
Huan works at a pizza restaurant in the morning he made 23 pizzas to sell at noon he had five pizzas left how many pizzas did he sell
Answers
Answer:
18. Huan sold 18 pizza's. 23 - 5 = 18.
You can also start at 23, and count down to 5.
Step-by-step explanation:
What is the measure of WV
(Value of x is 19)
Answers
i need answer please
Answers
Answer:
∠ BED = 57°
Step-by-step explanation:
angles on the circumference subtended by the same arc are congruent,
∠ BCD and ∠ BED are both subtended by arc BD , then
∠ BED = ∠ BCD = 57°
My sister needs help again MATHHH
Answers
Answer:
31
Step-by-step explanation:
PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction
This is just the order you do the operations.
First, Parentheses.
Second, Exponents,
Third, Multiplication or Division
Last, Addition or Subtraction
So we have,
[6(20) + 3(15)] ÷ 5
We first look at Parentheses.
The first case is 6(20)
6(20) = 120
We have [120 + 3(15)]÷ 5
We solve 3(15) as its the next parentheses
3(15) = 45
We have [120 + 45] ÷ 5
Then we solve for [120 + 45] as it's in brackets.
[165] ÷ 5 = 31
The answer is 31.
Which table represents a function?
X y
-4 6
0 8
4 12
X y
-4 3
-2 6
-2 9
X y
-3 7
-1 9
-3 -7
X y
1 2
1 6
2 10
Answers
Answer:
-2x+4>18.
Step-by-step explanation:
Solve and graph a one variable inequality. Solve the inequality and graph the solution on a number line.
Evaluate a+4a+4a, plus, 4 when a=7a=7a, equals, 7
Answers
(But if not it’s 60)
Answer:
the answer is 11
Step-by-step explanation:
Find the value of x
x =
Answers
Answer:
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of x.}[/tex]
[tex]\textsf{The value of x is an angle for this triangle.}[/tex]
[tex]\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}[/tex]
[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]
[tex]\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}[/tex]
[tex]\textsf{other times, and most of the time they're not. These are called Equilateral}[/tex]
[tex]\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}[/tex]
[tex]\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}[/tex]
[tex]\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}[/tex]
[tex]\textsf{equation where x is the \underline{subject}.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}[/tex]
[tex]\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}[/tex]
[tex]\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}[/tex]
[tex]\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}[/tex]
[tex]\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}[/tex]
[tex]\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}[/tex]
[tex]\underline{\textsf{We should have;}}[/tex]
[tex]\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}[/tex]
[tex]\textsf{We should remove the negative for x by dividing the whole equation by -1.}[/tex]
[tex]\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}[/tex]
[tex]\underline{\textsf{Simplify the right side of the equation;}}[/tex]
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)
Answers
Answer:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2[/tex]
And we want to find:
[tex]\displaystyle (f\circ g)(-1)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f\circ g)(-1) = f(g(-1))[/tex]
Hence, find g(-1):
[tex]\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}[/tex]
Substitute:
[tex]\displaystyle f(g(-1)) = f(1)[/tex]
Find f(1):
[tex]\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
Suppose that there are two types of tickets to a show advance and same day the combined cost of one advance ticket and one same-day ticket is $70 for one performance 20 advance tickets and 35 same day tickets were sold.The total amount paid for the tickets was $1850.what was the price of each kind of ticket
Answers
The price of the advance ticket is $40 and the price of the same day tickets is $30.
What are the linear equations that reperesent the question?a + b = $70 equation 1
20a + 35b = 1850 equation 2
Where:
a = cost of one advance ticket
b = cost of one same day ticket
What is the cost of one same day ticket?
Multiply equation 1 by 20
20a + 20b = 1400 equation 3
Subtract equation 3 from equation 2
15b = 450
Divide both sides by 15
b = $30
What is the cost advance ticket?
Subtract $30 from $70.
$70 - $30 = $40
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
When finding an indefinite integral, your answer must include:.
Answers
Answer:
is the set of infinitely many primitives that a function can have. It is represented by ∫ f(x) dx. It reads: integral of x differential of x. ∫ is the integration sign.
Answer 12 please thank you
Answers
Answer: 30%
Step-by-step explanation:
because my friend said so? <3
hope this helps!
Which two terms in (3+14) +27 could you add to get a multiple of ten?
Answers
Answer:
3 and 27
Step-by-step explanation:
Step 1: Determine which two terms we can use
We have the following numbers to choose from: 3, 14, 27
Adding two numbers to get a multiple of ten means that the number that we come up with needs to be divisible by ten. For example: 20, 30, 50, 100 are all multiples of ten.
In this example the only one that would add up to create a multiple of ten is 27 and 3 which would give us 30 which is a multiple of 10.
Answer: 3 and 27
A museum receives an average of 488 visitors per day. The museum 15 open every day. A. Estimate the number of visitors the museum receives during a month.
Answers
An estimate of the number of visitors that vist the museum during a month given the average number of visitors per day is 15,128.
What is multiplication?
Multiplication is an arthmetic operation that can be used to determine the product of a number. The sign used to denote multiplication is x.
How many visitors does the museum have in a month?
In order to determine this value, multiply the average daily visitors by the number of days in a month
488 x 30 = 15,128
To learn more about multiplication, please check: https://brainly.com/question/13814687
Mr. Ramos's monthly mileage allowance for a company car is 750 miles. He drove 8 miles per day for 10 days, then went on a 3-day trip. The table shows the distance he drove on each day of the trip.
Trip Mileage
Day Miles Driven
Tuesday 156.1
Wednesday 240.8
Thursday 82.0
After the trip, how many miles remain in Mr. Ramos's monthly allowance? Record your answer in the box.
Answers
Answer:
558.9 miles total
Step-by-step explanation:
See attached spreadsheet.
If the quadratic equation x2 + 6x + 19 = 0 is rewritten in the form (x - p)2 = q ,
what is the value of p and q
Answers
Answer:
p = -3
q = -10
Step-by-step explanation:
[tex]x^{2}+6x+19=x^{2}+6x+9+10[/tex]
[tex]\text{we know that} \ x^{2}+6x+9=\left (x+3)^2\right\ \text{ because it is a special product}[/tex]
[tex]\text therefore \ ,\ x^{2}+6x+19=(x + 3)^2+10[/tex]
[tex]\text therefore \ ,\ x^{2}+6x+19=0 \ means\ (x + 3)^2= -10\ means\ (x -\ - 3)^2= -10[/tex]
A company makes an ice-cream treat in the shape of a hemisphere on top of a cone, as shown below.
2 cm
10 cm
Answers
Answer:
56/3 pi cm^3
Step-by-step explanation:
1/2 volume of sphere = 1/2 4/3 pi r^3
volume of cone 1/3 pi r^2 h
r =2 h = 10
result : 56/3 pi cm^3
The volume of the ice cream is 58.64 cubic cm.
What is a three dimensional figure?A three dimensional figure has three dimensions as length, breadth and height. The volume of a three dimensional figure is the amount of the substance contained by it.
Given that,
The height of cone part of the ice cream is h = 10 cm.
The radius of the hemisphere is r = 2 cm.
As per the diagram given the radius of the hemisphere is equal to the radius of cone as 2 cm.
The volume of hemisphere is given as (2/3) × πr³.
And, the volume of cone is given as (1/3) × πr²h.
Now, the volume of the ice cream treat is equal to the sum of the volume of cone and hemisphere as,
V = (1/3) × π × r²h + (2/3) × π × r³
Substitute the values to get,
V = (1/3) × π × 2² × 10 + (2/3) × π × 2³
= (56/3) × π
= 58.64
Hence, the volume of the ice cream treat is 58.64 cubic cm.
To know more about Three dimensional figure click on,
https://brainly.com/question/24303419
#SPJ2
Find the side ratio given
pls show work<3 :)
Answers
Answer:
5/2 See below
Step-by-step explanation:
L x W x H = 125/8
for a CUBE L W and H are the same
L^3 = 125/8
L = 5/2