The explicit rule for the geometric sequence is Tₙ = 9 (2/3)ⁿ⁻¹
What is a geometric sequence?A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, to discover the term before another in the geometric sequence, we just divide the term by the same common ratio. To get the next term in the geometric sequence, we must multiply with a fixed term.
Given, the geometric sequence 9,6,4,8/3
The nth term of the sequence is given as:
Tₙ = arⁿ⁻¹
a is the first term
n is the number of terms
r is the common ratio
From the given geometric sequence:
a = 9
r = 6/9 =2/3
Substitute
Tₙ = 9 (2/3)ⁿ⁻¹
Therefore, the explicit rule for the geometric sequence is Tₙ = 9 (2/3)ⁿ⁻¹.
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Daniel measures the growth of his tomato plant and records the results in the table.
What was the average rate of growth during this time period for his plant to thenearest tenth?
Answer:
1.2
Step-by-step explanation: it just is
help me please and thank you !
Answer:
if you want to solve this question download doubtnut app and solve this question please mark me as brainliest answer
This graph shows how fast a commuter train travels on its route in an urban area. What is the meaning of the point with an x-coordinate of 4
The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.
From the graph, the x coordinate 2, have a y coordinate of 120. Hence:
The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.
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Pls help me! Will give brainest to whoever is correct
Answer:
When x= 3,
2x => 6
5x+ 1 => 16
According to the pythagorus theorem,
hypotenus²= base² + height²
hypotenus²= 6² + 16²
hypotenus = √ 292 = 17.1
answer option no. 3
Answer:
2. 17.1 units
Step-by-step explanation:
x=3
2 x 3=6
5 x 3 + 1=16
6² + 16²=c²
36 + 256=c²
292=c²
\(\sqrt{292}\)=17.0880075
c=17.1
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing
Answer:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Step-by-step explanation:
Geometrically speaking, the area of a rectangle (\(A\)), in square centimeters, is described by following expression:
\(A = w\cdot l\) (1)
Where:
\(w\) - Width, in centimeters.
\(h\) - Height, in centimeters.
By Differential Calculus, we find an expression for the rate of change of the area of the rectangle (\(\dot A\)), in square centimeters per second:
\(\dot A = \dot w\cdot l + w\cdot \dot l\) (2)
Where:
\(\dot w\) - Rate of change of the width of the rectangle, in centimeters per second.
\(\dot l\) - Rate of change of the length of the rectangle, in centimeters per second.
If we know that \(w = 12\,cm\), \(l = 15\,cm\), \(\dot w = 4\,\frac{cm}{s}\) and \(\dot l = 9\,\frac{cm}{s}\), then the rate of change of the area of the rectangle is:
\(\dot A = \dot w\cdot l + w\cdot \dot l\)
\(\dot A = 168\,\frac{cm^{2}}{s}\)
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
Suppose you are given a rectangular piece of cardboard having length 6x+2 inches and width 2x−4 inches. Then you cut out a square from this piece of cardboard having side length x inches. Find the area of the remaining piece of cardboard expressed in terms of x.
To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.
Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.
The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.
This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16
Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.
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Identify a, b, and c in this equation.
3x (squared) + 4x + 2 = 0
Please hurry!
Answer:
A is 3 B is 4 and C is 2
Step-by-step explanation:
this is most likely right unless your usong a diffrent formula
What is the rate (i.e. Slope) between these two points? (-5,0) and (0, 6) *
will mark brainleist pls help
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
select the correct answer. of the students in gianna's math class, 28% of the students have Gianna's favorite book, and 36% of the students have seen the movie version of the book. she finds that 20% of the students have both read the book and seen the movie version. what is the probability that a randomly chosen student in gianna's math class has read her favorite book or seen the movie version of the book? (a) 44%, (b)64%, (c)24%, (d)84%.
As a result, the probability that a randomly selected student in Gianna's probability maths class has read or seen the movie adaptation of her favourite book is 44%.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.
solve this problem,
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = 28%
P(B) = 36%
P(A and B) = 20%
Using the formula, we can find:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 28% + 36% - 20%
P(A or B) = 44%
As a result, the probability that a randomly selected student in Gianna's maths class has read or seen the movie adaptation of her favourite book is 44%.
As a result, the right answer is (a) 44%.
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determine the surface area and volume
The surface area of a cylinder is 284m² and it's volume is 366.9m³
What is the surface area and volume of a cylinder?To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:
Surface Area (A) = 2πr² + 2πrhVolume (V) = πr²hFrom the given question, the data are;
radius = 4mheight = 7.3ma. The surface area of the cylinder is;
SA = 2π(4)² + 2π(4)(7.3)
SA = 283.999≈284m²
b. The volume of the cylinder is
v = πr²h
v = π(4)²(7.3)
v = 366.9m³
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Write an equation for the line with slope 4 and y- intercept 12
the eqaution of a line is:
y = mx + b
where,
y = y - coordinates
m = slope
x = x - coordinates
b = intercepts
so with the values given as:
m = 4
b = 12
so the equation of line with the given values is
y = 4x + 12
Which of the following theorems verifies that ABC-DEF?
AA
63°
63
C
D
OA: AA
OB. HA
OC. LL
D. HL
The theorem that justifies the similarity of the two triangles is given as follows:
A: AA.
What is the Angle-Angle Similarity Theorem?The Angle-Angle (AA) Congruence Theorem states that if two pairs of corresponding angles are congruent, then the triangles are similar.
In other words, if two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle must also be equal in measure, and the two triangles are therefore congruent.
The two pairs of corresponding angles that are congruent in this problem are given as follows:
63º and 63º.90º and 90º. -> right angle.Hence the third angle will also have the same measure for both triangles.
Hence the AA theorem can be used and the correct option is given by option A.
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In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoint a (3,8) and (1,-4)?
The answer is (2, 2) but how do I solve?
Answer:
\(M = (2,2)\)
Step-by-step explanation:
Given
\((3,8)\) and \((1,-4)\)
Required
Determine the coordinate of the midpoint (M)
This is calculated as thus:
\(M = \frac{1}{2}(x_1 + x_2, y_1 + y_2)\)
Where
\((3,8)\) -- \((x_1,y_1)\)
\((1,-4)\) -- \((x_2,y_2)\)
So, we have:
\(M = \frac{1}{2}(3 + 1, 8 - 4)\)
\(M = \frac{1}{2}(4, 4)\)
\(M = (\frac{1}{2}*4, \frac{1}{2}*4)\)
\(M = (2,2)\)
Hence, the coordinates of the midpoint is (2,2)
What is the frequency of the function f (x). f (x) = -2sin x/4 +3
Answer: \(8\pi\)
Step-by-step explanation:
The period is \(\frac{2\pi}{1/4}=8\pi\).
the accompanying data set contains two variables, x1 and x2. pictureclick here for the excel data file a. how many observations have x2 values equal to 2?
The variables 8 observations have x2 values of 2 or greater.
Two variables, x1 and x2, are present in the supplementary data set. There are a total of 20 observations in this data set. The x2 values for 8 of these 20 observations are equal to 2. Thus, x2 values of two were present in eight out of twenty observations, or 40%. The following 12 observations' x2 values do not add up to 2. Thus, 8 of the 20 observations in the data set have x2 values of 2 or higher.8 of these 20 observations have x2 values that are equal to 2. Thus, eight out of twenty observations, or 40 percent, had x2 values equal to two. The x2 values for the next 12 observations are not equal to 2. Consequently, 8 of the data set's 20 observations have x2 values of 2 or above.
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Recall that two angles are complementary if the sum of their measures is 90°.
Find the measures of two complementary angles if one angle is 18° more than two times
the other angle.
The smaller angle measures
...
Complementary angles - The smaller angle is 24 degrees in size.
what are complementary angles?
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
Let x equal the first angle's measurement for the sake of explanation.
Let y be the size of the first angle's complement.
One angle, which we'll refer to as y, is 18 more than twice as large as another, x.
y = 18 + 2x
Complementary angles add up to 90 degrees.
x + 18 + 2x = 90
By substituting for y,
we get x + 18 + 2 x = 90.
Putting like phrases together and taking 18 off on both sides...
3x + 18 = 90
- 18 -18
3x = 72
By dividing both sides by 3, you get
3x/3 = 72/3
24 degrees is the angle between the two that is smaller. and the other angle would be,
y= 18+2x
=18+2(24)= 66 degrees.
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A basketball roster is shown in the table.
A 4-column table with 7 rows titled Basketball Roster. Column 1 is labeled Player with entries Adams, Brock, Cup, Dennis, Early, Finn, Graham. Column 2 is labeled Grade with entries 11, 12, 11, 10, 12, 11, 12. Column 3 is labeled Position with entries G, F, F, G, C, F, G. Column 4 is labeled height with entries 5 foot 6, 5 foot 8, 5 foot 9, 5 foot 3, 5 foot 11, 5 foot 9, 5 foot 5.
Which variable would be classified as a continuous quantitative variable?
grade
height
player name
position
Using variable concepts, it is found that the player's height is a continuous quantitative variable.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, ...What are qualitative and quantitative variables?Qualitative variables: Assumes labels or ranks.Quantitative variables: Assume numerical values.In this problem:
The player name and position are qualitative variables.Grade assumes only integer values, hence it is discrete.The height is quantitative, assuming decimal values in inches, hence it is also continuous.You can learn more about continuous and discrete variables at https://brainly.com/question/16978770
Answer:
height
Step-by-step explanation:
noballz
Suppose that each quarter at a particular community college Jared has to pay $744 in tuition and $29 in fees.
If Jared has 4 quarters remaining, find the total amount he will need for tuition and fees.
Answer:
He will need to pay $3092 in both tuition and fees for the remaining 4 quarters.
Step-by-step explanation:
\(4(744+29)=\\4(773)=\\3092\)
Evaluate the line integral ∫ 4xy dx + 2x 2 − 3xy dy, where C is the arc of the circle x 2 + y 2 = 1, from (1, 0) to (0, 1) in the counterclockwise direction.
Refer to the images attached. Edit: I realized after uploading this answer that the integral in terms of y is MUCH easier, so I attached that as well :) But at least you know it can be done both ways!
4. Which expression represents the following calculation? Add 16 to the quotient of 72 and 8.
(72/8) + 16
9 + 16
= 25
U want to add 16 to the quotient so it should be written in parenthesis
Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter the scale factor as a fraction in simplest form.
The circles are similar because the transformation rule (_ , _) can be applied to Circle 1 and then dilate it using a scale factor of (_/_)
Answer
its scale factor is 4/3 and 0.75
Step-by-step explanation:
3600 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 25 years, to the nearest cent?
Answer:
31043.09
Step-by-step explanation:
answered on delta math and got it correct
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205 inches. If 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 205.3 inches? Round your answer to four decimal places.
Answer:
the probability is 0.0750
Step-by-step explanation:
The computation of the probability is shown below;
The mean of x is
= 1.5 ÷ √79
= 0.1688
Now the probability is
= P(Z < -0.3 ÷ 0.1688) + P(\bar{x} > 0.3 ÷ 0.1688)
= P(Z < -1.78) + P(Z > 1.78)
= P(Z < -1.78) + 1 - P(Z < 1.78
= 0.0375 + 1 - 0.9625
= 0.0750
hence, the probability is 0.0750
if ax-cd=a wat is x .......
Answer:
Option A:\( \frac{a + cd}{a} \)
Step-by-step explanation:
ax - cd = a
=> ax = a + cd
\( = > x = \frac{a + cd}{a} \)
Hence,
Option A is the answer.
Answer:
A. \(\frac{a+cd}{a}\)
Step-by-step explanation:
ax-cd=a
Add cd to both sides:
ax=a+cd
Divide both sides by a:
x=\(\frac{a+cd}{a}\)
10
If a translation of (x, y) - (x + 6, y - 10) is applied to
figure ABCD, what are the coordinates of D'?
O (-5,-2)
O (1, -12)
O (4, -15)
0 (-9, 6)
17
Save and Exit
Next
Submit
Mark this dretum
Answer:
without seeing the original D coordinates, I can't give an answer.
But if you take the original D coordinates and add 6 to the x value, then subtract 10 from the y value, you'll have the answer
Step-by-step explanation:
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
A restaurant uses 2 1/2 pints of broth for each pot of chicken noodle soup.
Drag the equation that correctly answers each question to the correct container.
How many pints are needed for 2 3/4 pots of soup?
Answer:
6 7/8
Step-by-step explanation:
Sorry if I got it wrong :/