The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:
∑4i = 0(5)(1/3)i
= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵
= 364/243
Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.
Answer:
The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Step-by-step explanation:
The given expression is
[tex]3n+3[/tex]
For n=1,
[tex]3(1)+3=6[/tex]
For n=2,
[tex]3(2)+3=9[/tex]
For n=3,
[tex]3(3)+3=12[/tex]
The required AP is
[tex]6, 9, 12, ...[/tex]
Here first term is 6 and common difference is 3.
The sum of n terms of an AP is
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{13}=\frac{13}{2}[2(6)+(13-1)(3)][/tex]
[tex]S_{13}=\frac{13}{2}[12+36][/tex]
[tex]S_{13}=312[/tex]
Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
6 numbers per cube
if one is a 1, then the other one has to be a 2, 4 or 6 to be an odd sum
1+2=3, 1+4=5,1+6=7
since there are 3 numbers you can get that would be a 3/6 ( reduce to 1/2) probability
so 1/2 probability
1/2 is wrong, I put it on my exam and got it wrong:/
Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table.
In which step did Susu first make an error?
Step 1
Step 2
Step 3
Step 4
The given Quadratic equation is
[tex]4x^2- 8x - 13 = 0\\\\4(x^2- 2 x - \frac{13}{4}) = 0\\\\ (x-1)^2-1^2- \frac{13}{4}=0\\\\ (x-1)^2=\frac{\sqrt{17}}{4}\\\\ x-1=\pm\frac{\sqrt{17}}{4}\\\\ x=1 +\frac{\sqrt{17}}{4} \text{or} x=1-\frac{\sqrt{17}}{4}[/tex]
These are the steps to determine the roots as well as solve the quadratic equation.
You can find the mistake by looking at the procedure of solving the quadratic equation by completing the square solved above.
Answer:
step 3
Step-by-step explanation:
For one week at your store, employees worked 200 regular hours and 50 hours of overtime. what percent of the total hours for the week were overtime?
total hours = 200+50 = 250
50 were overtime
50/250=0.20 = 20% of the hours were overtime
The original price P of an item less a discount of 20% ?
Answer:
0.8 P
Step-by-step explanation:
Let the origional price of P
A discount of 20% is given on the item
The price of item=[P(100-d)]÷100
The price of the item= [tex]\frac{p(100-20)}{100}[/tex]
The price of the item= [tex]\frac{p(80)}{100}[/tex]
The price of the item= 0.8 P
If the discount 20% is given on origional price of the item, than the price will be 0.8 P
Hence, the correct answer is 0.8 P
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 00 and 66 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes.
Which method(s) can be used to solve a system of equations? Select all that apply.
distributing
graphing
substitution
formulas
addition
modeling
Answer:graphong, substitution, addition
Step-by-step explanation:
Please help! Geometry.
In a community fitness group, 40% of members run for exercise and 36% of members run and play a sport. What percentage of members who run for exercise also play a sport?
By dividing the percentage of community fitness group members who run and play a sport (36%) by those who run for exercise (40%), we find that 90% of the members who run for exercise also play a sport.
To determine the percentage of community fitness group members who run for exercise and also play a sport, we can use the information provided. The question states that 40% of members run for exercise and 36% of members run and play a sport. To find what percentage of members who run also play a sport, we need to find the proportion of runners who are also sport players.
To do this, we divide the percentage of members who run and play a sport by the percentage who only run:
Percentage of runners who also play a sport = (Percentage of members who run and play a sport) / (Percentage of members who run for exercise)
So,
Percentage of runners who also play a sport = 36% / 40% = 0.9
We then multiply by 100 to convert this to a percentage:
0.9 × 100 = 90%.
Therefore, 90% of the members who run for exercise also play a sport.
The risk set by the researcher for rejecting a null hypothesis when it is true is called the
Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?
In this case or scenario,
the double-angle identity that should be used is the one for cosine.
In totality, we shall need the following three trigonometric
identities to end up with the equality:
1. cos (2a) = cos² (a) - sin² (a)
2. sin² (a) + cos² (a) = 1
3. tan² (a) + 1 = sec²
(a)
Using identities 1 and 2 on the left-hand side of the
equation, we get the following:
1 + cos (2a) = 1 + cos² (a) - sin² (a) = 2 cos² (a)
Recalling that cos² (a) = 1 / sec² (a) and applying identity
3, we find the following:
2 cos² (a) = 2 / sec² (a) = 2 / (1 + tan² (a))
Therefore giving us:
2 cos² (a) = 2 / (1 + tan² (a))
Answer:
Its C. cos2a=cos^2a-sin^2a on ed
the _____ of a central angle are two radii of the circle.
A. sides
B. arcs
C. verticals
D. measures
Answer:
A.Sides.
Step-by-step explanation:
The central angle is the angle made by any arc at the center of the circle.Central angle is formed by two rays from the centre which cuts the circle at two points .The part of the two rays which lie inside the circle is the radius of the circle .
We say :
The sides of a central angle are two radii of the circle.
Use the remainder theorem to determine the remainder when 3t2 + 5t − 7 is divided by t − 5. A. 93 B. 43 C. 107 D. 57
Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos(t)>0, tan(t)>0
What is the equation of a quadratic graph with a Focus of (8,-8) and directrix of y=-6
A point is on a circle if the distance from the center of the circle to the point is equal to the
a) area.
b)circumference.
c)radius.
d)diameter.
Amy wants to buy a pair of jeans that cost $65. Today the store is offering a straight discount of 25%. Calculate her savings and cost after the discount.
Answer:
Amy's discount is $16.25, and the cost after the discount is $48.75.
Step-by-step explanation:
Write an equation in point-slope form of the line having the given slope that contains the given point. m=5m=5, (4,3)
Alan bought a suit on sale for $558. This price was 28% less than the original price. What was the original price?
Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π 3 rad.
Final answer:
To find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3 rad, we need to differentiate the formula for the area of a triangle with respect to time.
Explanation:
Rate of Change of Triangle Area with Increasing Angle
To find the rate at which the area of the triangle is increasing, we need to differentiate the formula for the area of a triangle with respect to time.
The formula for the area of a triangle is given by: A = 0.5 × a × b × sin(C), where a and b are the lengths of the two sides and C is the angle between them.
By differentiating this formula with respect to time, we can find the rate of change of the area with respect to time.
When the angle between the sides is π/3 rad, substitute the length of the sides and the rate at which the angle is increasing, and solve for the rate of change of area.
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 12 + y
18x – 12y= 18
The size of angle aob is equal to 132 degrees and the size of angle cod is equal to 141 degrees. find the size of angle dob.
angle AOB = 132 and is also the sum of angles AOD and
DOB. Hence
angle AOD + angle DOB = 132° ---> 1
angle COD = 141 and is also the sum of angles COB and BOD. Hence
angle COB + angle DOB = 141° ---> 2
Now we add the left sides together and the right sides of equations 1 and 2
together to form a new equation.
angle AOD + angle DOB + angle COB + angle DOB = 132 + 141 ---> 3
We should also note that:
angle AOD + angle DOB + angle COB = 180°
Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180
and solving for angle DOB:
180 + angle DOB = 132 + 141
angle DOB = 273 - 180 = 93°
Mount Rushmore is a sculpture that was carved using a model with a scale of 1 in :1 ft. If the model of George Washington’s face was 5 ft tall, how tall is his face on Mount Rushmore?
The height of the face is 60 inch.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
As 1inch = 1ft,
then to find out how many inches is George Washington’s face.
As there are 12inch in a foot
=12*5
=60inches
Thus , his face is 60ft tall.
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A card is picked from a standard deck of 52 cards. determine the odds against and the odds in favor of selecting a 10
The odds in favor of drawing a '10' from a standard 52-card deck are 1 to 12, and the odds against are 12 to 1.
Explanation:In a standard deck of 52 cards, there are four '10' cards - one each of hearts, diamonds, clubs, and spades. Hence the probability of drawing a '10' is 4 out of 52, or simplified, 1 out of 13.
Therefore, the odds in favor of selecting a '10' (i.e., the probability of selecting a '10' versus not selecting a '10') are 1 to 12 because for each '10' card there are 12 others that are not '10s'.
The odds against selecting a '10' are simply the inverse of the odds in favor. That is, for every one time you may draw a '10', there are 12 other times when you would draw something else, hence the odds against drawing a '10' are 12 to 1.
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What is 7.75×10-1 in standard notation
What is a tangent of a circle
Help plzzzzz!!!!!!!!!!
Each week Rosario drive to an ice-skating rink that is 60 miles away. The road trip takes 2.75 hours. If he averages 55 mph on his way to the rink, which equation can be used to find X, the number of miles per hour he averages on his way home?
Answer: The number of miles per hour he averages on his way home is 36 mph.
Step-by-step explanation:
Since we have given that
Distance traveled by Rosario = 60 miles
Time taken for road trip = 2.75 hours
Speed at which he on his way to the rink = 55 mph
Let X be the speed at which he averages on his way home.
So, According to question, we get that,
[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]
Hence, the number of miles per hour he averages on his way home is 36 mph.
A dart hits the circular dartboard shown below at a random point. find the probability that the dart lands in the shaded square region. the radius of the dartboard is 11in, and each side of the shaded region is 4in.
Answer:
.13 or 13%
Step-by-step explanation:
P = area of shaded region/area of entire board
Entire area: 3.14 * (11 * 11) = 379.94
shaded area: 3.14 * (4 *4) = 50.24
p = 50.24/379.94 = .13 or 13%
Find the exact value of cos 75 by using a sum or difference formula
The exact value of cos 75 is (√6 - √2)/4 or 0.2588190.
What is Trigonometry?Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.
We have to find the exact value of cos 75.
So, The value of cos 75 degrees in decimal is 0.258819045.
Then,
cos 75°
= cos (1.3089)
= (√6 - √2)/4 or 0.2588190
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