List the first five terms of the sequence
an = 5(-1)/ n!
Answers
The first five terms of the sequence are \(-5, -\frac{5}{2}, -\frax{5}{6}, -\frac{5}{24}, -\frac{1}{24}\).
Given sequence is \(`an = 5\frac{(-1)} {n!}`.\)
We need to find the first five terms of the sequence. We know that the sequence is represented by an in which the value of n varies from 1 to infinity.
So, we will put the values of n = 1, 2, 3, 4 and 5 in the given formula to find the first five terms of the sequence.
First term, when \(n = 1\), \(a_{1} = 5\frac{(-1)} {1!}=-5\)
Second term, when \(n = 2\), \(a_{2} = 5\frac{(-1)}{2!} = -\frac{5}{2}\)
Third term, when \(n = 3\), \(a_{3} = 5\frac{(-1)}{3!} = -\frac{5}{6}\)
Fourth term, when \(n = 4\), \(a_{4} = 5\frac{(-1)}{4!} = -\frac{5}{24}\)
Fifth term, when \(n = 5\), \(a_{5} = 5\frac{(-1)}{5!} = -\frac{1}{24}\)
Therefore, the first five terms of the sequence are: \(-5, -\frac{5}{2}, -\frax{5}{6}, -\frac{5}{24}, -\frac{1}{24}\).
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Related Questions
a rectangular prism is filled exactly with 8,000 cubes. each cube has edge length 15 cm. what is the volume of the rectangular prism?
Answers
The volume of the rectangular prism is 18,000,000 cm³.
To calculate the volume of the rectangular prism, we need to determine the number of cubes that fit inside it and then multiply it by the volume of each cube.
Given that the rectangular prism is filled exactly with 8,000 cubes and each cube has an edge length of 15 cm, we can calculate the volume of each cube:
Volume of each cube = (15 cm)³ = 15 cm * 15 cm * 15 cm = 3,375 cm³
Since there are 8,000 cubes, we can multiply the volume of each cube by the number of cubes to find the total volume of the rectangular prism:
Volume of rectangular prism = 8,000 cubes * 3,375 cm³/cube = 27,000,000 cm³
Therefore, the volume of the rectangular prism is 27,000,000 cm³ or 18,000,000 cm³.
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50 POINTS!!
1. Find a polynomial that represents volume of the fish tank. Explain how you used the
properties of exponents to determine your expression.
HINT: The formula for the volume of a rectangular prism is = ℎ.
2. The volume of each hemisphere is represented by the polynomial 3 − 702 + 360 − 1800.
Explain how to rewrite your answer for question 1 to reflect the volume of the fish tank after the
hemispheres are installed. Then carry out your plan. Show your work.
3. Show that the binomial that represents the length of the fish tank is a factor of the polynomial
you wrote in question 1.
4. Is the binomial that represents the length of the fish tank a factor of the polynomial that
represents the volume of the fish tank after the hemispheres are installed? Support your answer
mathematically.
5. The sanctuary currently has 125 exotic fish. The average amount of the tank allotted for each fish is represented by the binomial (22 − 1). Are the dimensions of the new habitat adequate
for these 125 fish? Explain.
Answers
To ensure that the dimensions of the fish tank are adequate, we need to ensure that the volume of the fish tank is greater than or equal to 2625. Since we do not have any information about the dimensions of the fish tank,
What ensures dimensions of the fish tank are adequate?1. Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively. V = l^1 × w^1 × h^1 = lwh. Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
2. Then the volume of each hemisphere is (4/3)πr^3. Since there are two hemispheres, the total volume they take up is 2(4/3)πr^3 = (8/3)πr^3.
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
\(V_new = lwh - (8/3)πr^3\)
3.The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
\(V = lwh = l(wh) = l(q)\), where q = wh.
Therefore, l is a factor of V.
4. To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively.
Then the volume of the fish tank is V = lwh. We can use the properties of exponents to simplify this expression by multiplying the powers of the variables: \(V = l^1 × w^1 × h^1 = lwh\) . Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
The volume of each hemisphere is \((4/3)πr^3\) . Since there are two hemispheres, the total volume they take up is \(2(4/3)πr^3 = (8/3)πr^3.\)
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
V_new = l \(wh - (8/3)πr^3\)
The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
V = lwh = l(wh) = l(q), where q = wh.
Therefore, l is a factor of V.
To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Since there is a remainder of \(- (8/3)πr^3\) , we can see that l is not a factor of V_new.
5. The average amount of tank allotted for each fish is represented by the binomial \((22 − 1)\) . To determine if the dimensions of the new habitat are adequate for 125 fish, we need to check if the volume of the fish tank is greater than or equal to the space required for 125 fish.
Let the required space for each fish be v, then the total space required for \(125\) fish is \(125v\) . Substituting the given binomial, we have:
\(v = (22 - 1) = 21\)
Therefore, the total space required for 125 fish is \(125v = 125(21) = 2625\) . We cannot determine if it is adequate for the given number of fish.
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Mark has a yard in the shape shown the area of his yard is 100 square meters the bottom side (base) is 20 meters what is the distance from bottom to the top of the yard?
Answers
Answer:
5 meters
Step-by-step explanation:
because 100 meters divided by the base equals the Height so 100 divided by 20 = 5
if a boy is 159. 5 cm tall, what is the boy’s height expressed in inches?
Answers
After using the conversion from inches to centimeters and using the division we have found that if the child measures 159.5 cm then expressed in inches is 62.8 inches.
What is the conversion factor from inches to centimeters?To convert the boy's height from centimeters to inches, we can use the following conversion factor: 1 inch = 2.54 cm.
Here are the steps to convert the boy's height from centimeters to inches:
Therefore, the boy's height expressed in inches is 62.8 inches.
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Which are factors of x² - 4x - 5? Select two options.
(x - 5)
0 (x-4)
0 (x-2)
0 (x + 1)
0 (x + 5)
Answers
Answer:
(x-5) & (x+1)
Step-by-step explanation:
Answer:
(x - 5) and (x + 1)
Step-by-step explanation:
x² - 4x - 5
consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)
the factors are - 5 and + 1 , since
- 5 × + 1 = - 5 and - 5 + 1 = - 4 , then
x² - 4x - 5 = (x - 5)(x + 1)
To make an equation, you need the _________ and the y-__________. If you only have 2 points, first get the __________, then use point-slope form.
Answers
Answer:
To make an equation, you need the slope and the y-intercept. If you only have 2 points, first get the slope, then use point-slope form.
Explanation:
Equations written in slope-intercept form (y=mx+b) require two pieces of information: the slope and the y-intercept, which is where the line crosses the y-axis. Point-slope form also involves the slope, which can be found from the two given points.
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
X - 4
5X + 2
Answers
Step-by-step explanation:
i think is this the answer
5×-4=-20
-20+2=18
A zookeeper has a map of his grounds. He is trying to get to the
Slow Sloth Shelter. He knows he needs to walk three rows forward
and five rows to the left. If his map were a grid, the Slow Sloth
Shelter would be located at (5,-3). If he can walk at a rate of 3.1
miles per hour, which of the following equations would represent
this situation?
A. y-3 = 3.1(x+5)
B. y-5= 3.1(x+3)
C. y+3 = 3.1(x-5)
D. y+5= 3.1(x-3)
Answers
Answer:
a
Step-by-step explanation:
last year, Austin had $30,000 to invest he invested some of it an account that paid 8% simple interest per year,and she invest the rest in a bank account that paid 10% simple interest per year.after one year, he receives a total of $2,680 to invest.how much did he and invest in each account?first account:____$second account:___$
Answers
We can solve this problem using a system of linear equations, have in mind the expression for simple interest:
\(\begin{gathered} I=\text{prt} \\ I=\text{interest} \\ p=\text{principal} \\ r=\text{rate in decimal form} \\ t=\text{time in years} \end{gathered}\)Let x be the principal invested on the first account.
Let y be the principal invested on the second account.
\(\begin{gathered} x+y=30,000\rightarrow\operatorname{Re}present\text{ total invested (1)} \\ 0.08x+0.1y=2,680\rightarrow\operatorname{Re}present\text{ the rates and interest earned }(2) \end{gathered}\)We can solve the system by the method of substitution, isolate the variable y in equation (1):
\(y=30,000-x\text{ (1)}\)Now, substitute (1) into equation (2) to get x-value:
\(\begin{gathered} 0.08x+0.1(30,000-x)=2,680 \\ 0.08x+3,000-0.1x=2,680 \\ -0.02x=2,680-3,000 \\ -0.02x=-320 \\ x=\frac{320}{0.02} \\ x=16,000 \end{gathered}\)Austin invested $16,000 on the first account.
Then, substitute the x-value in the equation (1) to get y-value:
\(\begin{gathered} y=30,000-16,000 \\ y=14,000 \end{gathered}\)Austin invested $14,000 on the second account.
pls help w this question, it’s prob easy but I’m rlly lazy thx
Answers
Answer:
For Line T:
\(m = \frac{5 - 14}{2 - 0} = - \frac{9}{2} \)
Since Lines T and R are perpendicular, the slopes of these two lines are negative reciprocals. So Line R has slope 2/9. We have:
\(3 = \frac{2}{9} (4) + b\)
\( \frac{27}{9} = \frac{8}{9} + b\)
\(b = \frac{19}{9} \)
\(y = \frac{2}{9} x + \frac{19}{9} \)
So the equation of Line R is
y = (2/9)x + (19/9)
8* x + y + y; use x=9, and y = 10
Answers
Answer:
92
Step-by-step explanation:
8* x + y + y
Where
x=9, and y = 10
Solution=8×9+10+10
=72+20
=92.
So the answer is 92
Answer:
92
Step-by-step explanation:
plz refer the photo i have attached
write the largest open interval on which f is the antiderivative for f.
Answers
The largest open interval on which f is the antiderivative for f is called the indefinite integral of f, and it is denoted by ∫f(x)dx. This interval can be determined by finding all the antiderivatives of f and then taking the union of their domains. Note that the antiderivative of f is not unique, as it can differ by a constant, so the indefinite integral of f is only determined up to an arbitrary constant.
To find the largest open interval on which a function f is the antiderivative for f', we'll first need to know the function f' (the derivative of f). However, you didn't provide the function f' in your question.
To give you a general idea of how to approach this problem, follow these steps:
1. Given the function f'(x), find the critical points by setting f'(x) equal to 0 and solving for x.
2. Determine the intervals based on the critical points.
3. Check the behavior of f'(x) in each interval to see where it's continuous and increasing.
4. The largest open interval on which f is the antiderivative for f' will be the interval in which f'(x) is continuous and increasing.
If you provide the function f'(x), I can help you find the largest open interval for the antiderivative.
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don't understand at all
Answers
Step-by-step explanation:
you would have to add the the sides and use context to find out the blank rectangles
The integral 1 π(y2−y4) dy 0 represents the volume of a solid. Describe the solid.
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the y axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
Answers
The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.
In the cartesian coordinate system, a plane is divided into four areas by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.Use washer method:The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.
As we have mentioned, the washer method is an extension of the disk method. This technique is established so that we can also calculate for the volume of the solid returned by rotating the region bounded by two curves over the x and y axis.\($$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$\)
Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.
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Where did my dad go? He went to get milk but never came back
Answers
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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Explain why the binomials (x+5)(x+5) do NOT follow the special difference of square rules. No fake answers brainliest to correct answers.
Answers
Answer:
See below
Step-by-step explanation:
The difference of square rules is \(a^2-b^2=(a+b)(a-b)\), but given that the expression is \((x+5)(x+5)\) and not \((x+5)(x-5)\), it doesn't follow this rule.
Find the value of 42 - (-10)
*explain how to solve*
Answers
Answer: 52
Step-by-step explanation:
42-(-10) first since your multiplying the two negative signs with each other it turns into a positive and looks like 42+10 and 42+10=52
SHOW WORK FOR BRAINLIST DUE TODAY
Answers
The true or false values of the statements are:
The book is $18 : TrueGiselle can earn up to $18 pulling weeds for her grandmaGiselle's grandma pays her $1 for every 5 weeds she pullsGiselle does not have to use any of her own money toward the purchase of the book when she pulls 90 weedsGiselle only needs to pull 18 weeds to not use any of her own money: FalseHow to determine the true statements from the scenario?From the question, we have the graph which represents the given parameters that can be used in our computation
Analysing the graph, we have:
The graph crosses the y-axis at y = 18
This means that the y-intercept of the graph is
y-intercept = 18
This in other word mean that:
The cost of the book is $18
So, (a) is true
Also, the graph crosses the x-axis at x = 90
This means that the x-intercept of the graph is
x-intercept = 90
This in other word mean that:
Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden
So, (b) and (d) are true
The amount paid by her grandma is calculated as
Amount = 18/90
Amount = 1/5
So, (c) is true
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Help plz god bless you I’m handing out brianlest
Answers
\(\huge\boxed{(-2)^2x^3y^2}\)
___________________________________________________________
\(\boxed{Explanation}\)
\((-2)\;*(-2)=(-2)^2\\x*x*x=x^3\\y*y=y^2\\\\Add\;them\;all\;together\;and\;you\;get\;(-2)^2x^3y^2.\)
Hope it helps!
May i have brainliest?
\(\huge\boxed{Thanks,\;Plip.}\)
What is the length of the distance between the two points of (6, -2) and (3, 4)? Answer options attached, DUE IN 2 HOURS and will give BRAINLIEST!
Answers
Answer:
\(\sqrt{45}\)
Step-by-step explanation:
We can use the distance formula to find the distance between these two points. The distance formula is:
\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
We know that x1 is 6, x2 is 3, y1 is -2, and y2 is 4, so we can substitute inside the equation.
\(\sqrt{(3 - 6)^2 + (4 - (-2))^2} \\\\\sqrt{-3^2 +6^2} \\\\\sqrt{9 +36}\\\\\sqrt{45}\)
Hope this helped!
Consider equation (1) again, ln (wage) = β0 + β1 educ + β2 exper + β3 married + β4 black + β5 south + β6 urban +u
(a) Explain why the variable educ might be endogenous. How does this affect the estimated coefficients? Does the endogeneity of educ only affect the estimate of β2 or does it affect the coefficients associated with other variables?
(b) The variable brthord is birth order (one for the first-born child, two for a second-born child and so on). Explain why brthord could be used as an instrument for educ in equation (1). That is, does this variable satisfy the relevance and exogeneity conditions for it to be an appropriate instrument?
Answers
(a) The variable educ might be endogenous
(b) The variable brthord is birth order (one for the first-born child, two for a second-born child and so on) could be used as an instrument for educ in equation
a) The variable instruction might be endogenous because as compensation increases the income expansions which additionally make able to an individual more educating himself. So there is an opportunity for the instruction might be an endogenous variable.
The indigeneity may involve the 32 the coefficient of knowledge as well different variables like married, black, south, urban, etc.
b) There is a substantial high relationship exists between birth order and the status of teaching. it is more possible to have higher schooling with less the order of child-born and the birth order is autonomous of the error term as well with wage. So the variable "birth order" is a good variable to use as an agency for the endogenous variable instruction.
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A triangular prism is 15 feet long. It has a triangular face with a base of 10 feet the volume of the prism is 945 ft. What is the height of its triangular height
Answers
The height of the triangular face of a triangular prism with a length of 15 feet and a base of 10 feet, and a volume of 945 cubic feet is 12.6 feet."
The formula for the volume of a triangular prism is given by:
Volume = (1/2) x base x height x length
where base and height refer to the base and height of the triangular face, and length refers to the length of the prism.
Substituting the given values, we have:
945 = (1/2) x 10 x height x 15
Simplifying:
945 = 75 x height
Dividing both sides by 75:
height = 945/75
height = 12.6 feet
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an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and photographers. what is the probability that the artist chosen will be a painter or a 5 photographer? write your answer as a fraction.
Answers
The probability that the artist chosen will be a painter or a photographer is 3/4
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
To solve this exercise the formula and the procedure that we have to use for probability is:
probability= (achieving success / possible outcomes)
Achieving success = 7 painters + 5 photographer = 12
Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16
Applying the formula to calculate the probability we get:
probability= (achieving success / possible outcomes)
probability= 12/16
Simplifying:
probability= 3/4
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Charlie wants to order lunch for his friends. He'll order 6 sandwiches and a $3 kid's meal for his little brother. Charlie has $27. How much can he spend on each sandwich if they are all the same price?
Answers
Answer:
$4
Step-by-step explanation:
27 - 3 = 24
24 ÷ 6 = 4
have a goodnight! :)
Answer:
a) Answer: $4 or less
b) Inequality: 6x + 3 ≤ 27
Step-by-step explanation: took the quiz and got it right!
Which step is the first incorrect step in the solution shown below? Solve: 5(x + 2) = 6x + 12 Step 1: 5x + 2 = 6x + 12 Step 2: -x + 2 = 12 Step 3: -X = 10 Step 4: x = -10 O A. Step 1 OB. Step 2 C. Step 3 D. Step 4
Answers
Answer:
Step 1
Step-by-step explanation:
Correct solution step-by-step:
1. 5(x + 2) = 6x + 12
2. 5x + 10 = 6x + 12
3. 5x - 6x = 12 - 10
4. -x = 2
5. x = -2
if it is accepted that an observed association is a causal one, an estimate of the impact that a successful preventive program might have can be derived from:
Answers
The estimate of the impact that a successful preventive program might have can be derived from
attributable risk.
What is an attributable risk?In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.
Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.
The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.
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which of the following is true with regards to statistical analysis? which of the following is true with regards to statistical analysis? bivariate analysis is a special form of multivariate analysis. it examines the relation between two or more variables. regression analysis is a univariate analysis. multivariate analysis examines the relationship between one, two or more variables. univariate analysis involves the analysis of a single variable.
Answers
The correct option is: "Univariate analysis involves the analysis of a single variable."
The following statement is true with regards to statistical analysis:
Univariate analysis involves the analysis of a single variable.
The other statements are not entirely accurate:
Bivariate analysis is a form of multivariate analysis that examines the relationship between two variables, but multivariate analysis can involve more than two variables.
Regression analysis is a multivariate analysis technique that examines the relationship between one dependent variable and one or more independent variables.
Multivariate analysis involves the examination of the relationship between two or more variables, not necessarily one, two, or more.
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Find the volume of a pyramid with a square base, where the perimeter of the base is
10.4in 10.4 in and the height of the pyramid is 9.6 in
9.6 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
The volume of a pyramid with a square base can be found using the formula:
V = (1/3)Bh
where B is the area of the base and h is the height of the pyramid.
In this problem, we are given that the perimeter of the base is 10.4 in, which means that each side of the square base has a length of 10.4 in / 4 = 2.6 in. Therefore, the area of the base is:
B = (2.6 in)^2 = 6.76 square inches
We are also given that the height of the pyramid is 9.6 in.
Substituting these values into the formula for the volume of a pyramid, we get:
V = (1/3)(6.76 sq in)(9.6 in)
V = 20.416 cubic inches
Rounding to the nearest tenth of a cubic inch, the volume of the pyramid is approximately 20.4 cubic inches.
Systems requests do not deal with factors involved in improving service.
a. true
b. false
Answers
Convert the capacity of 5 liters
Answers
Based on the above, the capacity of a 5-liter tin is about 500 cm³.
What is the capacity?To be able to convert the capacity of a 5-liter tin to its volume in cm³, One need to use the conversion factor that is, 1 liter is equivalent to 100 cm³.
So, to be able to calculate the volume of a 5-liter tin in cm³, one have to multiply the capacity (5 liters) by the conversion factor (100 cm³/liter):
Volume in cm³ = 5 liters x 1000 cm³/liter
= 500 cm³
Therefore, the capacity of a 5-liter tin is about 500 cm³.
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See full text below
Convert the capacity of a 5 litre tin to its volume in cm³.1litre is equivalent to 100cm³