The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.
What is an infinite geometric series?An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
Given: S = 2a₁
a₁ be the first term
r be the common ratio
Let the equation be S = a₁/1-r
2a₁ = a₁/1-r
substitute the values in the above equation, we get
2 = 1/1-r
2 - 2r = 1
2r = 1
The value of r = 1/2
Therefore, the common ratio(r) be 1/2.
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Z is a standard normal random variable. what is the value of z if the areato the right of z is 0.0122?
As per question, ‘Z’ is a standard normal random variable. And the value of ‘z’ is [tex]0.9878.[/tex]
According to the question, the area to left of ‘z’ and the equation can be written as:
[tex]P(Z > z) =0.01222[/tex]
Therefore,[tex]P(Z < z) =1-0.01222=0.9878[/tex]
Now the desired z-score corresponding to z-table graph = [tex]2.25[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Suppose a trolley stops at a certain intersection every 14min . The first trolley of the day gets to the stop at 6: 43 A.M. How long do you have to wait for a trolley if you get to the stop at 8: 15 A.M.? At 3: 20 P.M.?
You will wait for 11 minutes
Find the number of minutes between 5:00am and 8:37am
60 mins in an hour.
8-5=3 hours
60x3=180+37=217 minutes
Divide 217 by 12 to see how many bus stops have already been made
217/12=18
18*12=216
217-216=1 minute
12-1=11 minutes
Therefore you will have to wait 11 minutes.
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which net represents this rectangular prism
Help Please
Every item in the Just a Dollar store is priced $1.00. When Jack opens the store, there is $125.00 in the cash register. When he counts the money in the cash register at the end of the day, the total is $935.00. If the sales tax rate is8 %, how many items were sold that day? ____ items we sold that day.
Based on the price of each item in the store and the total cash in the register at the end of the day, the number of items sold for the day was 750 items.
How many things were sold?The cash that the Just a Dollar store made for the day was:
= 935 - 125
= $810
The cost of the items sold, less the sales tax was:
= 810 / (1 + 8%)
= $750
If each item costs $1, then the number of items sold was:
= 750 / 1 per item
= 750 items
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Three personal watercraft vehicles launch from the same dock. The first vehicle leaves the dock traveling due northeast, while the second vehicle travels due northwest. Meanwhile, the third vehicle leaves the dock traveling due north.
The first and second vehicles stop about 300 yards from the dock, while the third stops about 212 yards from the dock.
(d) Write a coordinate proof to prove that the positions of all three watercrafts are approximately collinear and that the third watercraft is at the midpoint between the other two.
The line created by 1st and 2nd is making the same angle with 3rd so all three will be colinear and 3rd is the midpoint of 1st and 2nd.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
After that, we need to substitute the values of x's and y's into the coordinate geometry.
Given the condition making a graph as shown below,
Now in ΔAOC and ΔBOC, the angle x is the same.
Distance AO = BO and CO is common side.
So both triangles will be congruent.
Since all corresponding side of two congruent triangles is the same.
So,
AC = BC hence C will be the midpoint of A and B.
Hence "The line created by 1st and 2nd is making the same angle with 3rd so all three will be colinear and 3rd is the midpoint of 1st and 2nd".
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Two lines intersect at point P. If the measures of a pair of vertical angles are (2x-7)° and, (x+3)° determine x and the measures of the other two angles?
Answer:
x = 10
One angle is 13 and the other angle is 13
Step-by-step explanation:
Vertical angles have the same measurement, so set the angles equal to each other and solve for x.
2x - 7 = x + 3 Subtract x from both sides of the equation
x - 7 = 3 Add 7 to both sides of the equation
x = 10 Now use this to solve for both angles
2(10) - 7 =
20 - 7 =
13
x + 3
10 + 3 =
13
TRAVEL A car leaves Seattle traveling at a speed of 60 miles per hour. Two hours later, a second car leaves
Seattle traveling at a speed of 50 miles per hour. The cars' distances from Seattle at time t hours are shown in
the table.
CAR A B
Distance (miles) 60t 50(t-2)
After how much time t will the two cars be the same distance from Seattle?
O 5 hours
O 10 hours
O The cars will never be the same distance from Seattle.
O 12 hours
The correct option regarding when the two cars will have the same distance from Seattle is:
The cars will never be the same distance from Seattle.
When will the two cars be at the same distance from Seattle?The distances for each car are given according to the following function:
A(t) = 60t.B(t) = 50(t - 2).They will have the same distance when:
A(t) = B(t).
Hence:
A(t) = B(t)
60t = 50(t - 2)
60t = 50t - 100
10t = -100.
t = -10.
Time cannot assume negative values, hence the cars will never be the same distance from Seattle.
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12 hours
Step-by-step explanation:
Use the graph to determine the solution of the
inequality |x+1| + 2 > 5.
O (-∞,-4) (2,00)
(-4, 2)
O (0,3)
O
(-∞,0) (3,0)
DONE✔
(-∞,-4) U (2, ∞)
====================================================
Work Shown:
|x+1| + 2 > 5
|x+1| > 5 - 2
|x+1| > 3
x+1 > 3 or x+1 < -3
x > 3-1 or x < -3-1
x > 2 or x < -4
x < -4 or x > 2
The portion x < -4 translates to the interval notation of (-∞,-4)
It might be helpful to think of x < -4 as -∞ < x < -4
The x > 2 is the same as 2 < x and the same as 2 < x < ∞. This turns into the interval notation of (2, ∞)
Therefore, we end up with the solution set of (-∞,-4) U (2, ∞)
The U symbol is the union operator to glue together the two intervals.
How to place 7 2/11 on a number line
Rebecca needs 10 yards of fabric to make a quilt. She has one piece of fabric that is
2 yards and another piece of fabric that is 41 yards. How many more yards of
fabric does Rebecca need to make the quilt?
F
4/ yd
G
31 Y
33 yd
J 62 yd
H
yd
33 YARDS is the total length of fabric that Rebecca needs.
What exactly do you mean by YARDS?
a small, frequently walled, paved, and open to the sky area next to a structure: court; b: a building's or collection of buildings' grounds. a house's immediate surroundings, which are often grassy grounds.
A man's belt or girdle, as it was known, was originally one yard long. King Henry I of England established the yard as the distance between his nose and the thumb of his extended arm in the 12th century. It is 36 inches right now.
We must determine the length of fabric Rebecca needs to finish her quilt based on the provided facts.
The total length of fabric required is 10 yards
One piece of fabric is long. 2yards
Another piece of fabric is long 41
Let be the missing length. x
2+41+x=10
x=-33
the length of fabric that Rebecca need is 33.
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I need this answered please
Answer:
2m - 59 = Matt's savings
Points!!!!!!!!!!!!!!!!
Leah walks 13 miles in 6 hours .lee walks 5 miles in 3 hours .Hercules walks 36 miles in 8 hours which Person had the fastest pace
Answer: Hercules has the fastest pace
Step-by-step explanation:
L=Leah. l=lee. H=Hercules
**Since the speeds are in fractions, make the denominators the same.
L=13/6
l=5/3
l=(5*2)/(3*2)
l=10/6
H=36/8
H=(36*6/8)/(8*6/8)
H=(216/8)/(48/8)
H=27/6
27/6 > 13/6 > 10/6
H>L>l
Hercules has the fastest pace
With flu season coming up, josh decides to make get-well-soon kits. he has 12 cans of chicken soup and 18 boxes of tissue, which he wants to use to make identical kits with no materials left over. what is the greatest number of get-well-soon kits josh can make?
Using greatest common factor (GCF), Josh can make 6 identical get-well-soon kits.
The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.
If Josh has to distribute 12 cans of chicken soup and 18 boxes of tissue to make identical get-well-soon kits with no material left over, solve the amount of kits he could make by solving the GCF of 12 and 18.
List down the factors of each number.
12 : 1, 2, 3, 4, 6, 12
18 : 1, 2, 3, 6, 9, 18
Common factors : 1, 2, 3, 6
Greatest Common Factor : 6
Hence, without any left over material, Josh can make 6 identical kits.
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Write the specified type of proof. two-column proof
Given: ®C
Prove: ΔKML ΔJMH
Answer:
hi
Step-by-step explanation:
How do you work this problem out?
7 5/24 + 10 1/8=
Answer:
17 1/
Step-by-step explanation:
first you have to find a common denominator, so you multiply 1/8 by 3 and get 3/24. then you add the two numbers getting 17 8/24 but you have to simplify it so it's 17 1/
Question is below in the image. Please explain. Thanks
Answer:
E
Step-by-step explanation:
[tex]\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)[/tex]
which does not exist.
Simplify by combining like terms. 5 v-3(2-v)
The simplification by combining like terms of 5v-3(2 -v) is 8v - 6.
According to the given question.
We have an expression5v - 3(2 - v).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
5v - 3(2 - v).
Here 5v, and 3v both are the like terms.
So, we add coeffcients of v to simplify the given expression.
Therefore, the simplification of 5v -3 (2 -v ) is given by
5v - 3(2 - v)
= 5v - 6 + 3v
= 8v - 6
Hence, the simplification by combining like terms of 5v - 3(2 - v) is 8v - 6.
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find a point which satisfies the linear equation X + Y is equal to 8 measure on it is 3 times it services
Answer:
Step-by-step explanation:
the horizontal line is x and 8=x so the point has to be where 8 is in the horizontal line. Then y is 3 so the point is gonna be in the vertical line then you connect those two-points and you have your line.
Match the sequence to its equation
2, -4,-10, -16
Answer: 2, -4, -10. -16, ..., -6n+8 n=1, 2, 3, ...
Step-by-step explanation:
2, -4, -10, -16
a₁=2
a₂=-4
a₃=-10
a₄=-16
a₂-a₁=-4-2=-6
a₃-a₂=-10-(-4)=-6
a₄-a₃=-16-(-10)=-6
Hence, this is an arithmetic progression: a₁=2 d=-6
[tex]a_n=a₁+(n-1)d\\a_n=2+(n-1)(-6)\\a_n=2-6n+6\\a_n=-6n+8[/tex]
Write a two-column proof for each case of Theorem 10.6 Case 2
Given: P lies inside
Prove: m< ABC = 1/2 m AC
The length of an inscribed angle is half the length of the central angle. The circumscribed angle's measure is 180 degrees less the central angle's measure.
What is the inscribed angle and the circumscribed angle?In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It is also the angle formed by two given points on a circle at a given point on the circle.
The length of an inscribed angle is half the length of the central angle. The circumscribed angle's measure is 180 degrees less the central angle's measure.
m ∠ABC = m ∠ABD + m ∠DBC (∠ Addition Postulate)
m ∠ABD = 1/2 m(arc AD)
m ∠DBC = 1/2 m(arc DC)
(The measure of an inscribed ∠ whose side is diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = 1/2 m(arc AD) + 1/2 m(arc DC) (Substitution)
m ∠ABC = 1/2 [m(arc AD) + m(arc DC)] (Factor)
m(arc AD) + m(arc DC) = m(arc AC) (Arc Addition Postulate)
m ∠ABC = 1/2 m(arc AC) (Substitution)
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NEED NOW!!! WILL GIVE BRAINLIEST!!! 17-19!!!
For the given systems of equations, we have that:
17. The solution is: x = 3, y = 4.
18. The company can afford to promote 2 engineers to level II.
19. The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item 17, the system is:
3x + 2y = 17.4x - 2y = 4.Adding the equations, we can eliminate y and solve for x, hence:
7x = 21
x = 3.
Then the solution for y is given as follows:
3x + 2y = 17
3(3) + 2y = 17
2y = 8
y = 4.
For item 18, the variables are given as follows:
Variable x: number of level I engineers.Variable y: number of level II engineers.The company has 8 engineers, hence:
x + y = 8 -> x = 8 - y.
The company can afford to pay a total of $472,000 to the engineers, hence, considering the salaries(in thousands of dollars) of each:
56x + 68y = 472.
We want to solve for y, hence, since x = 8 - y:
56x + 68y = 472.
56(8 - y) + 68y = 472.
12y = 24.
y = 2.
The company can afford to promote 2 engineers to level II.
The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.
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Answer:
This is my other account. I just needed 1+ answers togive brainliest for the other person. dont mind this
Step-by-step explanation:
12 : 21 : 30 simplified to its lowest terms is
Answer:
4 : 7 : 10
Step-by-step explanation:
as 12, 21, 30 are all divisible by 3
hope this helps
I need to find out the quadrilateral of 78° k,L,N,M
Answer: ∠L = 102°
∠N = 78°
Step-by-step explanation:
Quadrilaterals can be classified into Parallelograms, Squares, Rectangles, and Rhombuses. Square, Rectangle, and Rhombus are also Parallelograms.
A quadrilateral is called a parallelogram, if both pairs of its opposite sides are parallel. AB ∥ DC and AD ∥ BC. So, ABCD is a parallelogram. A parallelogram having all sides equal, is called a rhombus.
Given data,
In □KLMN, side LM ∥ side KN, side KL ≅ side NM If ∠K = 78°
then find the measure of ∠L, and ∠N
side LM∥ side KN
Interior angles on the same side of the transversal are supplementary.
∠K + ∠L = 180°
78° + ∠L = 180°
∠L = 180° - 78°
∠L = 102°
Construction:
Draw LP ∥ MN
So, LM ∥ KN and LP ∥ MN
PLMN is a parallelogram
MN ≅ LP
Now MN = LP and MN = KL
LP = KL
∠LKP = ∠LPK = 78°
LP ∥ MN so,
∠MNP = ∠LPK = 78° (corresponding angles are equal)
∠L = 102°
∠N = 78°
Therefore,
∠L = 102°
∠N = 78°.
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Find the area of the polygon.
The area of the polygon is what?
Answer:
Area = 792 m
Step-by-step explanation:
You can cut the polygon into 2 rectangles.
Subtracting 18 from 60 can give you the length of rectangle A, so 42 will be the new length for rectangle A.
Multiply 6 and 42 to get 252 for the area of rectangle A.
Multiply 18 and 30 to get 540 for the area of rectangle B.
(You multiply to find the area.)
Lastly you add both areas, 252 + 540, and the final result is:
Area = 792 m
Please help I will give you 30 points
Step-by-step explanation:
520÷13=40..............
Answer:
The answer is C 40
Step-by-step explanation:
520/ 13 = 40
:) have a nice day
Express each fraction as a decimal to the nearest hundredth.
43/46
43/49= 0.93
To express each fraction into its decimal we need to bring 100 at the denominator.
Fraction = numerator\denominator
For example :
1> 4\5
= 4*20\ 5* 20
= 80\ 100
= 0.80
2> 1\4
= 1 *20\ 4 *20
= 20\ 100
= 0.20
3> 49/50
= 49*2/50*2
= 98/100
=0.98
There are some numbers where it is not possible to make the denominator 100
So by the process of division method, we can convert the fraction into decimal form
43/46
0.93
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A container holds 15,000 milliliters (mL) of water. How many liters is this?
1,000 mL = 1 L
Answer:
Step-by-step explanation:
15L
15000 divided by 1000
Answer:
15 liters
Step-by-step explanation:
1000=1
15000=x..... (cross multiply)
15000=1000x...... (divide both sides by 1000)
=15
Convert the rate of 10 yard per 5 minute to feet per hour
Answer:120 yards
Step-by-step explanation:
10/5=2 2*60= 120 yards
PLEASEEEEE HELPPPPPP
