Write an equation to fond the nth term of each sequence. Then find a9. 5,20,80
Answers
Answer: a₉ = 327,680
Step-by-step explanation:
This seems to be a geometric sequence.
The recursive relation for this type of sequence is:
aₙ = aₙ₋₁*r
Where r is a constant.
Then we also have:
aₙ/aₙ₋₁ = r.
then we can find the value of r if we take the quotient of different consecutive terms, for example, the quotient of the second and firs term is:
r = 20/5 = 4
And the quotient between the third and second term is:
r = 80/20 = 4
Then we can conclude that r = 4.
And also, the n-th term of this sequence can be written as:
aₙ = a₁*r^(n - 1)
such that:
a₁ = 5
r = 4
Then the n-th term of this sequence is:
aₙ = 5*(4)^(n - 1)
Then the term a₉ can be found if we just replace n by 9 in the above equation:
a₉ = 5*(4)^(9 - 1) = 5*(4)^(8) = 327,580
Related Questions
you are treating a 50-year-old man that was involved in a fire. he suffered 25% 2nd-3rd degree burns to the anterior chest, neck and face. he has singed nasal hairs, and you identify stridor on your primary survey. pulse oximetry is 88% on a 100% non-rebreather mask. a burn center is 45 miles away. the next most appropriate step prior to transfer is:
Answers
A 100% non-rebreather mask has a pulse oximetry reading of 88%. There is a burn centre 45 miles distant. the best course of action to do after transferring a serious burn side.
A 50-year-old man who was injured in a fire is being treated by you. He sustained 25% 2nd–3rd degree burns to his face, neck, and anterior chest. He has burned nasal hairs, and your initial survey reveals stridor.
Any damage that exceeds 10% in size should be treated in a similar manner, although significant burns are classified as those that encompass 25% or more of the total body surface area. Rapid evaluation is essential. Any blaze can be managed using the general strategy for a significant burn. The most crucial things are to take a thorough history.
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Question:
Cube A has a volume of 128 cm. If the edge lengths of cube B are half the size of the edge lengths of cube A, what is the volume of cube B?
cube A
cube B
V = 128 cm
V = ?
o 16 cm3
O 64 cm3
O 32 cm
Cannot be determined
Answers
Answer:
16 cm3
Step-by-step explanation:
4 x 4 x 8 = 128
2 x 2 x 4 = 16
Answer:16 cm
Step-by-step explanation:
Z x 8 = 32Z = _____ Find the missing factor.
Answers
Solving the equation ,
\(\begin{gathered} Z\times8=32 \\ Z=\frac{32}{8} \\ Z=4 \end{gathered}\)Which operator should be used to determine if a number is evenly divisible by 5?
Answers
Answer:
the answer would be a % because of the divisibility rule
Jerry owns 20 shares of stock valued at $23 each. One day, the price of the stock rose$2. It fell $1 on each of the next three days. The stock price rose$4 on the next day. What was the average daily gain or loss for a share of the stock over this time period? What was the total value of Jerry’s stock at the end of this time period?
Answers
The total value of Jerry’s stock at the end of this time period based on the information about the average will be $26.
How to calculate the value?.From the information, Jerry owns 20 shares of stock valued at $23 each. One day, the price of the stock rose$2. It fell $1 on each of the next three days. The stock price rose$4 on the next day.
This will be:
= $23 + $2 - 3($1) + $4
= $23 + $2 - $3 + $4
= $26
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Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?
Answers
Answer:
6 nickels and 9 quarters
Step-by-step explanation:
x- nickels
y- quarters
----------------
the 2 equations are:
x+y=15y-x= 3add up the 2 equations:
2y= 18 y=9then
x= 15-9x=65. Simplify the expression. √80x²y • √25xy^4
Answers
Answer:
i think the answer is 20√5x^3y^5
Solve the following equations in the forms asked.
Answers
Answer:
Below in bold.
Step-by-step explanation:
Vertex form.
y = a(x - h)^2 + k
The point (h, k) is the vertex so from the graph:
y = a(x - 1)^2 - 8
From the x -interesect we see that x = 6 when y = 0 so
0 = a(6 - 1)^2 - 8
25a - 8 = 0
a = 8/25
So the vertex form is
y = (8/25)(x - 1)^2 - 8.
Factored form:
y = (8/25)(x + 4)(x - 6)
- as -4 and 6 are the zeros of the equation.
Standard form:
From the factored form we have
y = (8/25)(x^2 - 2x - 24)
y = 8/25 x^2 - 16/25 x - 192/25
or (in decimal form):
y = 0.32x^2 - 0.64x - 7.68.
Which line from section 1 reveals Hawthorne's informal, fatherly tone for this story?
A. A boy used to be seen in the streets of Boston.
B. Ben was born in 1706; so that he was now about 10 years old.
C. His father, who had come over from england.
Answer if you're 100 percent sure, this is for a test.
Answers
an elisa for hepatitis c has 95 percent sensitivity and 90 percent specificity. this means that the test
Answers
It indicates that the test is highly accurate in correctly identifying individuals with hepatitis C (high sensitivity) and accurately ruling out individuals without the disease (high specificity).
Sensitivity and specificity are two important measures of a diagnostic test's performance. Sensitivity refers to the test's ability to correctly identify individuals who have the condition, while specificity refers to its ability to correctly identify individuals who do not have the condition.
In the case of the ELISA test for hepatitis C, a sensitivity of 95% means that the test will correctly identify 95% of individuals who actually have hepatitis C as positive. This indicates a high probability of detecting the disease when it is present.
On the other hand, a specificity of 90% means that the test will correctly identify 90% of individuals who do not have hepatitis C as negative. This suggests that there is a 10% chance of a false positive result, where individuals without the disease are mistakenly identified as positive.
Overall, the high sensitivity and specificity of the ELISA test for hepatitis C make it a valuable tool in the diagnosis and screening of individuals for this infectious disease. However, it is important to consider that no test is 100% accurate, and false results can still occur. Therefore, additional confirmatory tests may be required in certain cases to ensure accurate diagnosis and appropriate medical intervention.
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1.12 as a mixed number ?
Answers
Answer:
1 12/100
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
It can converted to 28/25 or 1 and 3/25
A milk vendor had 9¼ litres of milk. She sold 6½ litres of milk. How much milk remaine
Answers
Answer:
2.75
Step-by-step explanation:
9.25-6.5=2.75
9 1/4 - 6 1/2= 2 3/4 or 2.75
james and elaine share a box of sweet in the ratio 2:3 what fraction of sweets does james receive and elaine receive
Answers
Step-by-step explanation:
I think it should be
james 2/5
elaine 3/5
PLEASE HELP!!
I don’t know how to solve Law of Sines, it doesn’t make sense to me.
I’ll award the brainliest!
Answers
Find the circumference of a circle with radius, r = 6.5m.
Give your answer in terms of pie
Answers
Answer:
13π m
Step-by-step explanation:
circumference of a circle = 2πr
=2*π*6.5
=13π m
Answer:
13\(\pi\) m
Step-by-step explanation:
The formula for circumference is 2r\(\pi\), so...
2r\(\pi\)
2(6.5)\(\pi\)
=13\(\pi\)
Distributions of data can be characterized along three aspects or dimensions. Which aspect represents the spread or distribution of the data?
Answers
The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.
About the Distribution of Data:
The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.
The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.
Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.
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At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5. Write an equation that represents the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totaled $68.
Answers
The equation that represent the relationship of the coffees is 3x + 5y = 68.
How to represent situation with system of equation?At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.
The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:
where
x = number of medium coffees soldy = number of large coffees soldTherefore, the equation is as follows:
3x + 5y = 68
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Charles rolls a number cube and then chooses a card from a set of cards numbered 1 through 24. What is the probability that he will roll an even number and choose an odd-numbered card?
1/4
1/8
1/3
1/24
Answers
Answer:
1/4
Step-by-step explanation:
1/2 Chance to roll an even number
1/2 Chance to pick an odd-numbered card
1/2 * 1/2 = 1/4
An Animal shelter has fixed expenses of $750. Each animal in the shelter costs an additional $6 a week. During the summer months, the total weekly expenses are at least $1170. Write and solve an inequality that represents the number of animals at the shelter for expenses to be at least $1170 a week. (Please explain how you got the answer)
Answers
The inequality that represents the number of animals at the shelter for expenses to be at least $1170 a week is x ≥ 70.
To solve this problem, we need to start by setting up an equation that represents the total weekly expenses of the animal shelter. Let's call the number of animals in the shelter "x".
The fixed expenses are $750, and each animal costs an additional $6 per week, so the total weekly expenses can be represented by the equation:
Total Weekly Expenses = $750 + $6x
We also know that during the summer months, the total weekly expenses are at least $1170. So, we can set up an inequality to represent this:
$750 + $6x ≥ $1170
To solve for x, we can start by subtracting $750 from both sides of the inequality:
$6x ≥ $420
Then, we can divide both sides by $6 to isolate x:
x ≥ 70
This means that there must be at least 70 animals in the shelter for the total weekly expenses to be at least $1170.
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19. Graph the function 3x + 2y = 8 with the given
domain: (-2,0, 2, 4}
TEK 3C
Justify/Show your work:
Answers
Answer:
Step-by-step explanation:
In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.
pls help i well give brllant
Answers
The scale factor was used for each dilation are-
Part a: For ΔABC - scale factor = 2Part b: For ΔDEF - scale factor = 1/2Part c: For ΔGHJ - scale factor = 1/3Part d: For ΔKML - scale factor = 3Explain about the dilation:A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.
A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.
Part a: For ΔABC
Length AB = 2 units
Length A'B' = 4 units
A'B' = 2 *AB
Thus, For ΔABC - scale factor = 2
Part b: For ΔDEF -
Length DF = 2 units
Length D'F' = 1 units
D'F' = 1/2 DF
Thus, For ΔDEF - scale factor = 1/2
Part c: For ΔGHJ -
Length GH = 3 units
Length G'H' = 1 units
G'H' = 1/3 GH
Thus, For ΔGHJ - scale factor = 1/3
Part d: For ΔKML -
Length KM = 2 units
Length K'M' = 6 units
K'M' = 3*KM
Thus, For ΔKML - scale factor = 3
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suppose that the slope parameter in a simple linear regression model is β1 = 3.52. what does this suggest about the nature of the relationship between x and y?
Answers
A slope parameter of β1 = 3.52 in a simple linear regression model suggests that there is a positive and direct relationship between the independent variable (x) and the dependent variable (y).
Specifically, for every one unit increase in the independent variable (x), the dependent variable (y) is expected to increase by an average of 3.52 units. This indicates a positive linear association between x and y, implying that as x increases, y tends to increase as well.
The magnitude of the slope parameter (3.52) also indicates the steepness of the relationship. A larger slope suggests a stronger relationship, indicating that the change in y for a given change in x is relatively large.
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the unite rate of the ratio 12/5/3/10 is 8/1. Yes or no
Answers
Yes, the unit rate of the ratio 12/5/3/10 is 8/1 as per given in the problem.
What does unit rate mean?A unit rate is the price for one unit of a given quantity. With one as the denominator, we express this as a ratio. You would run 7 yards on average every second if you ran 70 yards in 10 seconds, for instance. The 70 yards in 10 seconds and the 7 yards in 1 second ratios are both rates, however the 7 yards in 1 second ratio is a unit rate.
Here, given that the unit rate for the ratio given is 8/1
We have to check whether the ratio is correct or not
So, (12/5)/(3/10)
=(12/5)×(10/3)
=8/1
Therefore, the ratio 8/1 is correct as per given in the sum
So, the answer is yes
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If you rolled two dice, what is the probability that you would roll a sum of 11? Give your answer as a simplified fraction. Enter the number that belongs in the green box.
Answers
Answer:
1/18
Step-by-step explanation:
There are only 2 ways to get an 11 out of 36 possible ways.
2/36 = 1/18
Answer:
2/36 = 1/18
Step-by-step explanation:
Write the quadratic equation in standard form.
Then solve using the quadratic formula.
1+ 4x + 3x2 = 0
HELPP
Answers
Answer:
x = − 1 3 − 1
Step-by-step explanation:
Solve the equation for x by finding a , b , and c of the quadratic then applying the quadratic formula. x = − 1 3 − 1
what is the value of 6(2b-4) when b+5?
Answers
Answer:
The value of 6(2b-4) is 36.
Step-by-step explanation:
Given expression: 6(2b-4)
To find the value of 6(2b-4) at b=5, we need to substitute the b=5 in the expression, we get
6(2(5)-4)
= 6(10-4)
=6(6)
= 6x6=36
⇒ 6(2(5)-4)=36
Answer:
The value of 6(2b-4) when b=5 is 36.
Step-by-step explanation:
Given expression: 6(2b-4). To find the value of 6(2b-4) at b= 5, we need to substitute the b=5 in the expression, we get….Therefore, the value of 6(2b-4) is 36, when b=5.
A quilter created the following shape to use in a block for a new quilt. A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches. What is the area of the shape for the quilt block? seventy-three and three fifths in2 forty-one and four fifths in2 eighty-three and three fifths in2 one hundred forty-seven and one fifth in2
Answers
Answer:
(a) seventy-three and three fifths square inches
Step-by-step explanation:
You want to know the area of the quilt block shape shown.
Composite shapeThe shape can be considered to be composed of a rectangle 10.6 inches long, together with a right triangle with side lengths 4 and 5 inches.
AreaThe relevant area formulas are ...
triangle: A = 1/2bh
rectangle: A = bh
ApplicationThe area of the triangle is ...
A = 1/2(5 in)(4 in) = 10 in²
The area of the rectangle is ...
A = (10.6 in)(6 in) = 63.6 in²
The total area is ...
10 in² +63.6 in² = 73.6 in²
The area of the shape is 73 3/5 square inches.
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If In a = 2, ln b = 3, and In c = 5, evaluate the following: (a) In(a)= (b) In √b¹c-4a-2 = (c) In(a²b-³) In(be) ¹ = (d) (In c¯1¹)(ln)4 =
Answers
To evaluate the given expressions, let's substitute the given values:
(a) ln(a) = ln(2) = 0.69314718056
(b) ln(√(b¹c-4a-2)) = ln(√(3¹(5-4(2)-2))) = ln(√(3¹(5-8-2))) = ln(√(3¹(-5))) = ln(√(-15))
Note that the natural logarithm is not defined for negative numbers, so ln(√(-15)) is undefined.
(c) ln(a²b-³) ln(be)¹ = ln((2²)(3⁻³)) ln(e) = ln(4) ln(e) = 1 ln(e) = 1
(d) (ln(c⁻¹))⁴ = (ln(5⁻¹))⁴ = (ln(1/5))⁴ = (-ln(5))⁴
The value of (-ln(5))⁴ will depend on the approximation used for ln(5) but can be calculated using a calculator.
Please note that the expressions involving the natural logarithm may result in undefined values or require specific approximations for accurate calculations.
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t (minutes) = 0, 4, 7, 9.
r(t) (gallon per minutes) = 9, 6, 4, 3.
Water is flowing into a tank at the rate r(t), where r(t) is measured in gallons per minute and t is measured in minutes. The tank contains 15 gallons of water at time t = 0. Values of r(t) for selected values of t are given in the table above. Using a trapezoidal sum with the three intervals indicated by the table, what is the approximation of the number of gallons of water in the tank at time t = 9? (A) 52
(B) 57 (C) 67 (D) 77 (E) 79
Answers
The approximation of the number of gallons of water in the tank at time 9 min. is 52 gallons.
Using the trapezoidal sum, the approximation of the number of gallons of water in the tank at time t = 9 is given by:
Approximation =\([((t_1 - t_0) / 2) * (r(t_0) + r(t_1))] + [((t_2 - t_1) / 2) * (r(t_1) + r(t_2))] + [((t_3 - t_2) / 2) * (r(t_2) + r(t_3)))]\)
where \(t_0 = 0, t_1 = 4, t_2 = 7, t_3 = 9\).
Substituting the given values of r(t), we get:
Approximation = [((4 - 0) / 2) * (9 + 6)] + [((7 - 4) / 2) * (6 + 4)] + [((9 - 7) / 2) * (4 + 3))]
= (2 * 15) + (1.5 * 10) + (1 * 7)
= 30 + 15 + 7
= 52
Therefore, the approximation of the number of gallons of water in the tank at time t = 9 is 52 gallons. The answer is (A) 52.
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Line L_{1} has equation y = 3 - 2x Line L_{2} is parallel to L_{1} and passes through the point
(5, 2)Find the equation of L_{2} giving your answer in the form y = mx + c
Answers
The equation of line L₂, which is parallel to line L₁: y = 3 - 2x and passes through the point (5, 2), is y = -2x + 12.
Since line L₂ is parallel to line L₁, they have the same slope. The slope of line L₁ is -2. Therefore, the slope of line L₂ will also be -2.
We can use the point-slope form of a linear equation to find the equation of line L₂. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
We are given that line L₂ passes through the point (5, 2) and has a slope of -2. Substituting these values into the point-slope form, we have y - 2 = -2(x - 5).
Simplifying the equation, we get y - 2 = -2x + 10.
To express the equation in the form y = mx + c, where m is the slope and c is the y-intercept, we rearrange the equation as y = -2x + 12.
Therefore, the equation of line L₂ is y = -2x + 12.
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