The first term of the given arithmetic sequence is 7. This can be determined by finding the common difference and moving backwards from the third term using this value.
Explanation:The subject of this question is Arithmetic Sequence which is a topic in mathematics. An arithmetic sequence is defined by a common difference (d) between consecutive terms.
To solve this problem, we have to find the common difference first. The difference between the 8th term (56) and the 3rd term (21) is 35. But since there are 5 steps from the 3rd term to the 8th term, each step (or the common difference) must be 35 ÷ 5 = 7.
Now that we have the common difference (7), we can reverse it from the 3rd term (21) back to the 1st term which gives us: 21 - 2(7) = 7. So, the first term is 7.
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Suppose a and b are independent events. if p(a)=0.4 and p(b)=0.1, what is p(a u
b.?
To find the probability of the union of two independent events, use the formula P(A U B) = P(A) + P(B). In this case, P(A U B) = 0.4 + 0.1 = 0.5.
Explanation:To find the probability of the union of two independent events, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Since the two events, A and B, are independent, the probability of their intersection, P(A ∩ B), is 0. This is because the occurrence of one event does not affect the occurrence of the other event. Therefore, we have:
P(A U B) = P(A) + P(B)
Substituting the given values, we get:
P(A U B) = 0.4 + 0.1
= 0.5
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determine the heat energy received per kilogram of steam produced
An object is thrown from an initial height of 0 feet with an initial velocity of 160 feet per second. Solve for when it will return to the ground. Show your work and explain the steps used to solve.
x+3menor que 8 qual o resultado
x+3<8
8-3 =5
X<5
any number less than 5 will work
11. Edgar Anderson earns $200 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is zero and the value of b is not zero. Where could point P be located on the coordinate plane?
Select one or more:
x-axis
Quadrant IV
y-axis
Quadrant I
Quadrant II
Quadrant III
Answer:
y axis and
Step-by-step explanation:
The point P(a, b) where the value of a is 0, hence point P is located on the y axis.
Coordinate planeThe coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.
A point on the coordinate plane is located using the x and y coordinates.
Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.
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Rita borrowed 8000 at a rate of 10.5% compounded monthly assuming she makes no payments how much willshe owe after8 years
To avoid distortion of extreme values, a good indicator would be the A. mean. B. weighted-mean. C. mode. D. median
To avoid distortion of extreme values, a good indicator would be the
B. median.
Find the point on the line y = 3x + 2 that is closest to the origin.
The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
Given, [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].
Let [tex]m[/tex] is the slope of the line perpendicular to the above line.
So,
[tex]3\times m=-1\\m=-1/3[/tex]
Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].
So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].
Then the closest point will be the intersection point of these two lines, i.e.
[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]
and
[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]
Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
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what is 795840000 in a scientific notation
A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (6x + 1) wide by (4x - 3) long. The dimensions of the spa are (4x + 5) wide by (x + 6) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
How do i simplify this?
What is the greatest angle measure in the diagram?
95˚
105˚
119˚
180˚
The solution is, The greatest angle measure is angle F which is 119°
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
The sum of all the angles of a quadrilateral is 360°
(15x-10)°+(15x+14)°+(9x-4)°+(11x+10)° = 360°
Open up the brackets and rearrange the expression
15x-10°+15x+14°+9x-4°+11x+10°=360°
15x+15x+9x+11x-10°+14°-4°+10° = 360°
50x+10°=360°
Collect like terms
50x=360°-10°
50x=350°
Divide by the coefficient of x
x= 350/50
X=7°
Substitute the value of x into the various angles
15x-10°=(15×7)-10= 105-10=95°
15x+14°=(15×7)+14=105+14=119°
9x-4°=(9×7)-4=63-4=59°
11x+10°=(11×7)+10=77+10=87°
The greatest angle measure is angle F which is 119°
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Kholdy enterprises' outstanding bonds mature in 6 years, have a par value of $1,000, and make an annual coupon payment of $60. the market yield on the bond is currently 10%. what is the bond's price?
Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?
If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years
May has 31 days
there are 365 days in a year
31/365 probability someone has a birthday in May
The probability of the event A that represents that the man's birthday is in May is 0.084.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomely selected.
Assume that the Event A represents that the man's birthday is in may.
Total number of days in the month of may = n(A) = 31
Total number of days in a year = n(S) = 365
Therefore, the probability that the man's birthday is in may will be -
P(A) = n(A)/n(S)
P(A) = 31/365
P(A) = 0.084
Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.
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Outside diameter of a pipe is five and 7/32 inches the wall of the pipe or 5/32 inches thick find the inside diameter
5 7/32 = 167/32
5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32
167/32 - 10/32 = 157/32
= 4 29/32
Which polygon has an interior angle sum of 1080°?
The polygon which has an interior angle sum of 1080° is an Octagon
Interior angles of a PolygonFrom the question, we are to determine which polygon has an interior angle sum of 1080°
To find that, we will determine the number of sides the polygon has.
From the formula for sum of the interior angles in a polygon
Sum of interior angles = (n-2)180°
Where n is the number of sides
Then,
1080° = (n-2) 180°
1080° ÷ 180° = n-2
6 = n-2
n = 6 + 2
n = 8
A polygon with 8 sides is called an Octagon
Hence, the polygon which has an interior angle sum of 1080° is an Octagon
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There are 65 people who want to go on a tea cups ride at an amusement park. There are 10 tea cups that each seat 4 people. How many people need to wait before they get to go on the ride?
An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').
The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?
PLEASE HELP
If AD is median in triangle ABC and BD=24, then CD is:
24.
12.
6.
None of the choices are correct.
To solve this problem, let us first define what a median is. A median is a line segment that connects a vertex and the midpoint of the side opposite to that vertex.
In this case, the vertex is point A while the opposing side is side CB. Since it connects to the midpoint of CB, therefore this means that the median AD equally divides side CB into 2 parts. Since the length side CB is the sum of the lengths side CD and side BD. Therefore this means that:
length of CD = length of BD
length of CD = 24
Answer:
24
a squared + b - c ÷ m , if a=6 , b= 8 ,c = 5 and m = 3. Is it 12 , 13, 14, or 15?
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
A total of
644
tickets were sold for the school play. They were either adult tickets or student tickets. There were
56
fewer student tickets sold than adult tickets. How many adult tickets were sold?
martin brought 30 shares of microsoft at the close price of $24.53. In a few years, Martin sells all of his shares at $33.71. How much money did martin make?
Answer:
Money did martin make = 275.4 $
Step-by-step explanation:
Martin brought 30 shares of Microsoft at the close price of $24.53.
Number of shares = 30
Cost per share = 24.53 $
Total cost = 30 x 24.53 = 735.9 $
Martin sells all of his shares at $33.71
Selling price per share = 33.71 $
Total selling price = 30 x 33.71 = 1011.3 $
Gain for Martin = 1011.3 - 735.9 = 275.4 $
Money did martin make = 275.4 $
Megumi earned a salary of $39,312 last year. How much did she earn per month
2 months in a year
39312/12 = 3276 per month
Answer:
She earned $ 3,276 per month.
Step-by-step explanation:
We know that,
1 year = 12 months,
Given,
Megumi earned a salary of $39,312 last year
⇒ His salary of one year = $ 39,312
⇒ Salary of 12 months = $ 39,312
[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]
Hence, she earned $ 3,276 per month.
A company has a sales revenue of $10,000, cost of goods sold of $4500, and other operating expenses of $1500. what is this company's pre-tax income?
Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money
Answer:
The correct matches are:
1. impulse - a sudden stirring to do something
2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.
3. naught - nothing, nonexistence
4. renown - fame ; the condition when you are known or talked about by many people.
5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.
6. thrifty - careful with money . Like a person is thrifty about his own time.
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?