Which explicit formula is equivalent to a1 = 1, an = -6an-1
The explicit formula that is equivalent to aₙ = -6aₙ₋₁ is; aₙ = 1(-6)ⁿ⁻¹
What is the explicit formula?We are given;
a₁ = 1
aₙ = -6aₙ₋₁
Thus, for second term;
a₂ = -6a₁
a₂ = -6
For the third term;
a₃ = -6a₂
a₃ = 36
The resulting sequence is 1, -6, 36,......
The sequence is a geometric sequence with;
a = 1
r = -6
The explicit rule will be aₙ = 1(-6)ⁿ⁻¹
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. 40% of students passed 90% students attended class 30% both passed and attended class martin was selected at random he attend class daily determine the probability that he passed the exam
Probability that Martin passed the exam when he attend the class daily is given by 1/3.
Probability is the possibility to occurrence of an event.
In other words, Probability is the ratio of number of favorable cases under an event to total number of cases under that event.
Let P be the event that Martin passed the exam and A be the event that he attend the class daily.
Given that,
40% of students passed tbe exam.
The probability to pass the exam is given by,
[tex]P(P)=40%=\frac{40}{100}=\frac{4}{10}[/tex]
90% students attend the class daily
probability to attend the class daily is given by,
[tex]P(A)=90%=\frac{90}{100}=\frac{9}{10}[/tex]
30% student both passed the exam and attended class
So probability to both passed the exam and attend the class is given by,
[tex]P(P\cap A)=30%=\frac{30}{100}=\frac{3}{10}[/tex]
Now conditional probability that Martin will passed the exam if he attend class daily is given by,
[tex]P(P|A)=\frac{P(P\cap A)}{P(A)}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}[/tex]
Hence the required pobability that Martin passed the exam when he attend the class daily is given by 1/3.
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Graph the image of this figure after a dilation with a scale factor of 12centered at the point (−3, 0)
Answer:
bro tbh just use like or
Step-by-step explanation:
its not that deep
Triangle ABC is isosceles.
Triangle A B C. Angle A is x degrees, angle B is 118 degrees, angle C is x degrees. Sides A B and B C are equal.
Which equation can be used to find the degree measure of Angle A?
118 = x + x
x + x + 118 = 180
118 + 180 = x + x
(x + x) minus 118 = 180
Step-by-step explanation:
118+2×=180
180-118=62
62÷2(×)=31
×=31
Answer:
x + x + 118 = 180
Step-by-step explanation:
...........
How do you simplify 6 by the power of negative 2 multiplied by 6 by the power of 3
Answer:
Keep in mind the rules.
When we multiply terms with same bases we keep one base and add the exponents.
Step-by-step explanation:
[tex] = {6}^{ - 2} \times {6}^{3} \\ = { 6}^{ - 2 + 3} \\ = {6}^{1} \\ = 6[/tex]Hope this helps.Y<2/3x+2
A. (0,3)
B. (-3,1)
C. (3,5)
D. (1,2)
The ordered pair on the inequality y < 2/3x + 2 is D. (1,2)
How to determine the ordered pair?The inequality is given as:
y < 2/3x + 2
Next, we test the options:
A. (0,3)
3 < 2/3 * 0 + 2
3 < 2 --- false
B. (-3,1)
1 < 2/3 * -3 + 2
1 < 0 --- false
C. (3,5)
5 < 2/3 * 3 + 2
5 < 4 --- false
D. (1,2)
2 < 2/3 * 1 + 2
2 < 2.67 --- true
Hence, the ordered pair on the inequality y < 2/3x + 2 is D. (1,2)
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(x + 1 < 4) ∩ (x - 8 > -7).
The correct answer is x = 2
Inequality(x + 1 < 4) ∩ (x-8>-7)
Make x the subject in each case:
(x<4-1)(x>-7+8)
(x<3)∩(x>1)
If x<3, then x could be 2, 1, -1, etc.
If x>1, then x could be 2, 3, 4, etc.
Thus (x<3)∩(x>1) = 2
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Answer:
x = 2
Step-by-step explanation:
Hello!
We are looking at the intersection of two sets, or common values found between two sets of data.
We can solve for x on each side and find any common values between.
Find the Intersection[tex](x + 1 < 4) \cap(x - 8 > -7)[/tex][tex](x < 3)\cap(x > 1)[/tex][tex](x = 2, 1, 0, -1, -2...)\cap(x = 2, 3, 4, 5, 6...)[/tex][tex]x = 2[/tex]As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.
Therefore, the intersection of these sets is 2.
y + 3x ≤7
solve it…… …
Answer:
[tex]x \leq \frac{7 - x}{3}[/tex]
Step-by-step explanation:
This expression is an inequality which is a relation that makes a non-equal comparison between two numbers/expressions
we want x to be alone in one side, y + 3x ≤ 7
Subtract y from both sides,
y + - y + 3x ≤ 7 - y
3x ≤ 7 - y
divided both sides by 3 to get x alone
3x / 3 ≤ 7 - y / 3
x ≤ 7 - y / 3
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What is the value of x?
Answer: 5
Step-by-step explanation:
By the inscribed angle theorem.
[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]
there are three consecutive odd integers. Three times the largest is 7 times the smallest. WHat are the integers
Answer:
3, 5, 7
Step-by-step explanation:
We can assign the first number as x. Since all the numbers are odd the next number will be x+2, and the last will be x+4.
3*(x+4) = 7(x)
3x+12 = 7x
12 = 4x
x = 3
x+2 = 5
x+4 = 7
A rectangular quilt is to be made so that the length is 1.2 times the width. The quilt must be between 72ft^2 and 96ft^2 to cover
the bed. Determine the restrictions on the width so that the dimensions of the quilt will meet the required area.
W is the width of the quilt, the restrictions are given by the inequality:
7.7ft ≤ W ≤ 8.9 ft
How to determine the restrictions on the width?
Remember that for a rectangle of length L and width W, the area is:
A = L*W
In this case, we know that:
L = 1.2*W
Replacing that we get:
A = 1.2*W²
And we know that the area must be between 72 square feet and 96 square feet, then:
72ft² ≤ 1.2W² ≤ 96ft²
Now we can divide all by 1.2:
(72ft²)/1.2 ≤ W² ≤ (96ft²)/1.2
60ft² ≤ W² ≤ 80ft²
If we apply the square root in the 3 sides of the inequality, we get:
√60ft² ≤ √W² ≤ √80ft²
7.7ft ≤ W ≤ 8.9 ft
These are the restrictions on the width such that the quilt will meet the required area.
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Which of the following is the graph of the inequality y < 2x + 3?
Answer: A
Step-by-step explanation:
The line has a positive slope.
Eliminate B and D.Also, the line should be shaded below.
Eliminate C.This leaves us with D.
What is the slope of the line shown below??
Answer:
1
Step-by-step explanation:
We can find the slope using the slope formula, which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
The order of the points doesn't matter, but the points that are farthest right (8, 8) can be our y2 and x2 and the points that are farthest left (5, 5) can be our y1 and x1.
Thus, we have [tex]\frac{8-5}{8-5}=\frac{3}{3}=1[/tex]
Pls helppppppppppppppp
Answer:
y = 4/5x + 2
Step-by-step explanation:
Standard equation given slope and y-intercept -> y = mx + b
After substituting variables m and b, you get y = 4/5x + 2.
Jorge wants to determine the enlarged dimensions of a digital photo was 800 pixels high. The new photo will be 1,260 pixels wide .what will the new height be
The height of the new photo must be 945 pixels (option B).
How to calculate the width of the new photograph?To calculate the height of the photograph, we must first know what proportion the sides of the previous photo have, for this we do the following operation:
600 × 100 = 60,00060,000 ÷ 800 = 75According to the above, the height of the photo is equal to 75% of the width. So to find the height of the new photograph we must do the following operation:
1.260 ÷ 100 = 12.612.6 × 75 = 945So the height of the new photo should be 945 pixels.
Note: This question is incomplete. Here is the missing part:
Question
Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?
Options
460 pixels
945 pixels
1,680 pixels
1,860 pixels
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vincent ordered pizza for him and his wife for dinner. when they had finished, they realized that 5/8 of the pizza was gone. for lunch the next day, vincent decided to eat 1/4 of what was left. how much was left after lunch?
Answer:
1/8 of the pizza
Step-by-step explanation:
whole pizza=1
5/8 is gone so 1-5/8=8/8-5/8=3/8
3/8-1/4 = 3/8-2/8=1/8
hope this helps
If a coin is tossed, a die is rolled, and a candy is taken from a dish of 20 candies, 7 of which are red, what is the probability of getting a red candy, a heads, and a 2 on a 6-sided die?
ANSWER OPTIONS:
0.0167
0.29167
1.0167
0.029167
Answer:
B
Step-by-step explanation:
7/20 x 1/2 x 1/6
Insurance protects you from liability and allows you to provide for your own and others' long-term needs. But what if you never need the insurance? You wind up putting out a lot of money and you get nothing out of it. Which kinds of insurance do you think are worth the cost? Which are not?
Life , Health , Car are considered to be very important insurance , Rental Car Damage , Travel Insurance has no usage.
What is Insurance ?Insurance is safe guarding any thing which has some monetary or emotional value to it , It can be life , health , car , house , your gold etc.
Insurance protects you against something you can never predict .The life is unpredictable and Insurance is a cover to that .
As given in the question , a person can be lucky enough that he never gets to use the money that he invested in the Insurance , but not investing due to this is wrong.
This is not difference of opinion but lack of prediction of future and lack of understanding the needs of life.
Life , Health , Car , Home , Fire etc . insurance that protects the basic amenities of life are considered to be very important ,
while nowadays insurance of Rental Car Damage , Travel Insurance , these are some which has no usage beyond the fact that they cover nothing.
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Given:
\overleftrightarrow{BD}
BD
B, D, with, \overleftrightarrow, on top is the perpendicular bisector of segment \overline{AC}
AC
start overline, A, C, end overline.
\overline{BD}
BD
start overline, B, D, end overline is 333 units long.
\overline{AC}
AC
start overline, A, C, end overline is 888 units long.
Naomi was asked to show that point DDD is equidistant from points AAA and CCC.
A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points A and C.
BD ⊥ AC (given)
BD = 3 units, and AC = 8 units.
BD is the perpendicular bisector of segment AC (given)
Thus,
<BDA ≅ <BDC (right angles formed by a perpendicular bisector)
AD ≅ DC (equal parts of a bisected line)
AD ≅ DC = 4 units
Thus joining points B to A, and B to C,
BA ≅ BC.
So that applying Pythagoras theorem to ΔABD, we have:
[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]
[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]
= [tex]\sqrt{25}[/tex]
AB = 5 units
So that,
BA ≅ BC = 5 units
Therefore, it can be concluded that point D is equidistant from points A and C.
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Please help ill give whoever answers the best the brainliest answer :)))
Answer:
w(w-5)
Step-by-step explanation:
Given Width of rectangle = w
Length of rectangle is 5 less than width of rectangle = w - 5
Area of Rectangle = Length x Width = w * w-5 = w(w-5)
Answer:
the second answer option
Step-by-step explanation:
the area of a rectangle is
length × width
or
l × w
l = w - 5
so, when we use the second in the first equation, we get
(w - 5)×w
or
w(w - 5)
helllppppppppppp please
Answer:
h = 5t
Step-by-step explanation:
So basically, its a slope problem again. You are trying to find the equation that equals hits. So you can cross off t = 5h and t = h + 5. So now, you need to find the most reasonable answer by calculating the slope.
If you try h = t + 5,
Put in 3 - you get 8
Put in 7 - you get 12
But on the table you get 15, 36 respectively.
If you try h = 5t,
Put in 3 - you get 15
Put in 7 - you get 35
Which is much closer to the numbers in the table, therefore it is the answer.
what does 4r-8=6r+14 equal to?
Answer:
r is -11
Step-by-step explanation:
Move the like terms to the same side. 4r-6r is -2r
14 + 8 is 22
22/-2 is -11
A spherical ball is inflated so that it’s radius increases in the ratio 4:3. Find the ratio in which it’s volume is increased
Answer:
64:27
Step-by-step explanation:
If the ratio between the old and new radius is described with the ratio: 4:3, then if the first radius was 3, then the new radius is 4.
Also if you multiply 3 by (4/3) it also equals 4
The volume of a sphere is described as: [tex]\frac{4}{3} \pi r^{3}[/tex]
So let's plug in 3 and 4 and see their ratio.
[tex]\frac{\frac{4}{3}\pi 4^{3} }{ \frac{4}{3}\pi 3^{3} }} = \frac{4^{3} }{3^{3} } = \frac{64}{27}[/tex]
The answer is 64/27 or (4/3)^3
Answer:
by a factor of 64/27 or 64:27
Step-by-step explanation:
Volume of a sphere = 4/3 pi r^3
now increase the radius by 4/3 ( this is 4:3)
new volume = 4/3 pi (4/3 r)^3
= 64/27 * 4/3 pi r^3
so the original volume is increased by 64/27
(-1,8) and (8,5). this is a coordinate distance wuestion that i rly need help on
Answer:
3[tex]\sqrt{10}[/tex] ≈ 9.45
Step-by-step explanation:
calculate the distance d between the points using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (8, 5 )
d = [tex]\sqrt{(8-(-1))^2+(5-8)^2}[/tex]
= [tex]\sqrt{(8+1)^2+(-3)^2}[/tex]
= [tex]\sqrt{9^2+9}[/tex]
= [tex]\sqrt{81+9}[/tex]
= [tex]\sqrt{90}[/tex]
= [tex]\sqrt{9(10)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]
= 3[tex]\sqrt{10}[/tex] ← exact value
≈ 9.49 ( to 2 dec. places )
PLEASE HELPP I NEED ASAP
Answer:
[-6, -2](-2, 1](1, 5]Step-by-step explanation:
The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.
ObservationThe first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.
The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.
Bottom pieceThe first part of the function definition is ...
f(x) = -4
This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...
-6 ≤ x ≤ -2
In interval notation, a square bracket is used when the end point is included in the interval.
f(x) = -4 if x ∈ [-6, -2]
Middle pieceThe second part of the function definition is ...
f(x) = -3
This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...
-2 < x ≤ 1
We use a round bracket (parenthesis) when an end point is not included in the interval.
f(x) = -3 if x ∈ (-2, 1]
Top pieceThe third part of the function definition is ...
f(x) = 4
This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...
1 < x ≤ 5
In interval notation, this is ...
f(x) = 4 if x ∈ (1, 5]
Select the value that completes the perfect square trinomial: x^ 2 +22x+_____
Answer:
121 i.e. 11²
Step-by-step explanation:
(a+b)² = a² + 2ab + b²
x² + 2 × x × 11 + 11² = (x + 11)²
can you help me i give you brainly
Answer:
Step-by-step explanation:
it should be sth like green graph
Suppose $n$ is a positive integer such that $6n$ has exactly 9 positive divisors. How many prime numbers are divisors of $6n$
The number of prime divisors of "6n" is 2 numbers 2 and 3
Given
"n" = 6
thus 6n = 6(6) = 36
The positive divisors are 1, 2, 3, 4, 6, 9, 12, 18 and 36
So, the number of prime divisors of "6n" is 2 numbers 2 and 3.
The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.
The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.
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Solve for this trig identity step by step.
Using trigonometric identities, and equality is reached, hence the equality is proved.
Which trigonometric identity are used to solve this question?These three identities are used:
[tex]\sin^2{x} + \cos^2{x} = 1 \rightarrow \cos^2{x} = 1 - \sin^2{x}[/tex].[tex]\sec^2{x} = 1 + \tan^2{x}[/tex].[tex]\sec^2{x} = \frac{1}{\cos^2{x}}[/tex]Hence:
[tex]\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}[/tex]
[tex]\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}[/tex]
[tex]\sec^4{x} = \sec^2{x} \times \sec^2{x}[/tex]
[tex]\sec^4{x} = \sec^4{x}[/tex]
Equality is reached, hence the equality is proved.
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What is the constant rate of change of the table below? Please help
Answer:
4 m/s
Step-by-step explanation:
Well the constant rate of change can be defined as the slope or rise/run. This can be calculated using any two points. So I'll use (10, 40) and (20, 80). the seconds increased by 10 (run) and the meters increased by 40 (rise) This gives you the equation 40/10 which simplifies to 4. That is the constant rate of change