If a₁ = 6 and an
an-1 + 3 then find the value of a4.
Answers
Answer:
a₄ = 15
Step-by-step explanation:
using the recursive relation \(a_{n}\) = \(a_{n-1}\) + 3 and a₁ = 6 , then
a₂ = a₁ + 3 = 6 + 3 = 9
a₃ = a₂ + 13= 9 + 3 = 12
a₄ = a₃ + 3 = 12 + 3 = 15
Related Questions
Given:
p: Two linear functions have different coefficients of x.
q: The graphs of two functions intersect at exactly one point.
Which statement is logically equivalent to q-p?
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one
point.
O If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect
at exactly one point.
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same
coefficients of x.
O If the graphs of two functions intersect at exactly one point, then the two linear functions have the same
coefficients of x.
Answers
Answer:
Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B? The initial values of the two functions are different, and the rates of change of the two functions are also different. The initial values of the two functions are different, and the rates of change of the two functions are the same. The initial values of the two functions are the same, and the rates of change of the two functions are different. The initial values of the two functions are the same, and the rates of change of the two functions are also the same.
I need help with this
Answers
The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3
For the equation to be true, two scenarios need to be considered:
When the expression 6x-3 is positive and equals 3:
6x-3 = 3
When the expression 6x-3 is negative and equals -3:
6x-3 = -3
By solving these two equations, we can find the equivalent statement:
Solving 6x-3 = 3:
Adding 3 to both sides gives us:
6x = 6
Dividing both sides by 6:
x = 1
Solving 6x-3 = -3:
Adding 3 to both sides gives us:
6x = 0
Dividing both sides by 6:
x = 0
Therefore, the equivalent statement to |6x-3|=3 is:
6x-3=3 or 6x-3=-3, which can be further simplified to:
6x-3=3 or 6x-3=-3
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An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 837 new employees. If a new route is not granted, it will hire only 199 new employees. If the probability that a new route will be granted is 0.37, what is the expected number of new employees to be hired by the airline?
Answers
Considering a discrete distribution, it is found that the expected number of new employees to be hired by the airline is of 446.16.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, considering the situation described in the text, the distribution is given by:
P(X = 837) = 0.37.P(X = 199) = 0.63.Hence, the expected value is given by:
E(X) = 0.37(867) + 0.63(199) = 446.16.
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In a village, 80% of people are Hindus and 2% are Muslims. If 36 people do not follow these two religions, by drawing a Venn diagram find the number of the Hindu.
Answers
Explanation:
Assuming the two religions are mutually exclusive, this would mean 80%+2% = 82% of people are either Hindu or Muslim (but not both).
The remaining 100% - 82% = 18% of people are neither religion mentioned.
x = number of people in the village
18% of x = 36
0.18x = 36
x = 36/0.18
x = 3600/18
x = 200
Then,
80% of x = 0.80*x = 0.80*200 = 160 people are Hindu
The Venn diagram is shown below.
Three people spend money on a vacation. The expression −1,0263 represents the amount of money each person spends on the vacation. Which expression is equivalent to −1,0263 ?
Answers
Answer:-(-1,026/3
Step-by-step explanation:
when the ___ calculates an increasing ___ ; the ___ may choose to decrease .
Answers
The answer that correctly fills the missing portions is option A.
The full sentence is: When the Bureau of Labor Statistics (BLS) calculates an increasing Consumer Price Index (CPI); the Federal Reserve (FED) may choose to Quantitative Easing.
Quantitative easing is a monetary policy operation in which a central bank buys government bonds or other financial assets to infuse monetary reserves into the economy in order to encourage economic activity.
The goal of QE is to level the playing field in order to make spending and investing money more enticing and accessible to people. Lower interest rates may improve the possibility that company and civilian borrowers will borrow to make purchases, promoting economic activity.
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Full Question:
When the ___ calculates an increasing ___ ; the ___ may choose to decrease______.
A) BLS, CPI. FED, QE
B) OECD, QE, BLS, CPI
C) BEA, GDP, BLS, CPI
D) BEA, CPI, OECD, GDP
Match each drawing on the left with its geometric notation on the right. Some of the answer choices on the right may not be used.
Answers
Answer:
Please attach a photo to this so I can better answer your question
Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adults were randomly selected and their preferences recorded. (Round your answers to three decimal places.)
(a)
What is the probability that more than 7 preferred McDonald's?
(b)
What is the probability that between 2 and 7 (inclusive) preferred McDonald's?
(c)
What is the probability that between 2 and 7 (inclusive) preferred Burger King?
Answers
B)0.6563
C)0.6563
Solve for x. Round to the nearest tenth, if necessary.
Answers
Using Trigonometry, the value of x in the right triangle is 17.1
Since we have a right angle triangle ; The angle L can be obtained thus ;
L = 180 - (90+67)
L = 23
Using Trigonometry:
Sin23° = opposite/ hypotenuse
Opposite= 6.7
hypotenuse= x
Sin23° = 6.7/x
x = 6.7/sin(23°)
x = 17.14
Therefore, the value of x to the nearest tenth is 17.1
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Find the volume of the rectangular prism.
4 ft
6 ft
5 ft
Answers
The volume of the prism is 120 ft (one hundred twenty).
What is the volume of the prism ?
To find the volume of a blockish prism, multiply its 3 confines length x range x height.
The volume is expressed in boxy units. The formula for the volume of a prism is V = B h, where B is the base area and h is the height. The base of the prism is a cube.
The length of the cube is 9 cm and the range is 7 cm. The face area of a prism is given as S = ( 2 × Base Area)( Base border × height) where" S" is the face area of the prism.
Here,
Length = 4
Breadth = 6
Height = 5
Volume = 4 x 6 x 5 = 120
Thus,
The volume of the prism is 120 ft (one hundred twenty).
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Generally those who are less active have no opportunities to exercise
Answers
Answer:
False
Step-by-step explanation:
Edge 2021
A state lotto has a prize that pays $900 each week for 20 years.
Find the total value of the prize: $
If the state can earn 5% interest on investments, how much money will they need to put into an account
now to cover the weekly prize payments?
Reminder: There are 52 weeks in a year.
Answers
The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
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I really don’t understand graphs
Answers
2) A 25 foot ladder leans against a house. The base of the ladder is 7 feet
away from the house. What is h, the height of the house? #2 pleasee
Answers
Step by step
Using Pythagorean theorem, we can find the height of the right triangle
We know a= 7, we know c= 25, we need to find b
a^2 + b^2 = c^2
7^2 + b^2 = 25^2
49 + b^2 = 625
Subtract 49 from both sides to solve b
49 - 49 + b^2 = 625 - 49
b^2 = 576
Take square root of both sides
√ b^2 = √ 576
b = 24 ft
Now according to the drawing, the ladder did not go to the top of the house, we need to add 11 ft to 24 ft = 35 ft total height
Imagine that we know the following information for populations living in cities and rural areas. In big cities, average commutes are 40 minutes with a standard deviation of 15 minutes. In rural areas, the average commute is 25 minutes with a standard deviation of 6 minutes. Who has a longer commute, Mary from the city who travels for 35 minutes or Jean from the country who travels 30 minutes? a. Jean, because her commute is in the country. b. Mary, because city traffic moves slowly c. Mary's commute is 5 minutes longer d. Jean, because she travels 30 minutes on slow country roads
Answers
Answer:
a. Jean, because her commute is in the country.
Step-by-step explanation:
Z-score:
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score will have the longer commute.
Mary:
Travels for 35 minutes. In big cities, average commutes are 40 minutes with a standard deviation of 15 minutes. This means that \(X = 35, \mu = 40, \sigma = 15\). So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{35 - 40}{15}\)
\(Z = -0.33\)
Jean:
Travels for 30 minutes. In rural areas, the average commute is 25 minutes with a standard deviation of 6 minutes. This means that \(X = 30, \mu = 25, \sigma = 6\). So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{30 - 25}{6}\)
\(Z = 0.83\)
Due to being in the Country, Jean's z-score is higher, so her commute is longer. The correct answer is given by option A.
The true statement is (a) Jean, because her commute is in the country.
For Mary, we have the following parameter:
x = 35 minutes from the city
For Jean, we have the following parameter:
x = 30 minutes from the county
The z-score is calculated as:
\(z = \frac{x - \bar x}{\sigma}\)
For the city, we have:
\(\bar x = 40\)
\(\sigma = 15\)
So, the z-score of Mary is:
\(z = \frac{35 - 40}{15} = -0.33\)
For the country, we have:
\(\bar x = 25\)
\(\sigma = 6\)
So, the z-score of Jean is:
\(z = \frac{30 - 25}{6} = 0.83\)
0.83 is greater than -0.33
Hence, Jean has a longer commute
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Six more than a number,
n, is less than fourteen. Which inequality represents this relationship?
Answers
Answer:
6 + n < 14
just in case...
n < 8
What is Metric Conversions?
Answers
I think it’s 40%, am I correct?
Answers
my thought process is
There are 100 ticks (20 spaces with 5 marks)
the area it wants has 6 large spaces (6*5=30) and 3 marks
30+3 is 33
Use the rule for order of operations to simplify the expression as much as possible:
22−2(9⋅2−8)
Answers
22+(-18*-2+16)
22+36+16
74
74 is the answer
Which of the following makes the equation true?
b/4 = 16
A. 64
B. 4
C. 16
D. 8
Answers
Answer:
the answer is A
Step-by-step explanation:
cross multiply 16×4 =64
.In a simple physical apparatus, distances u cm and v cm are connected by the formula 1/u+1/v=1/3
Given the u-distance is increasing at the rate of 2 cm s',
Find the rate at which the v-distance is changing, in cm s', when u-4 cm.
Answers
The rate at which the v-distance is changing is -18 cm/s when u = 4 cm.
To find the rate at which the v-distance is changing, we can use implicit differentiation. Given the equation:
1/u + 1/v = 1/3
Differentiating both sides of the equation with respect to time (t), we get:
(d/dt)(1/u) + (d/dt)(1/v) = (d/dt)(1/3)
Using the chain rule, the left-hand side becomes:
(du/dt) / u^2 - (dv/dt) / v^2 = 0
Since we know that du/dt = 2 cm/s, and we want to find dv/dt when u = 4 cm, we can substitute these values into the equation:
(2) / (4^2) - (dv/dt) / v^2 = 0
Simplifying the equation:
1/8 - (dv/dt) / v^2 = 0
Now, we can solve for dv/dt:
(dv/dt) / v^2 = -1/8
dv/dt = -v^2 / 8
To find the rate at which the v-distance is changing, we need to substitute the value of v when u = 4 cm. From the given equation, we can rearrange it as follows:
1/u + 1/v = 1/3
1/v = 1/3 - 1/u
1/v = (u - 3) / (3u)
v = (3u) / (u - 3)
When u = 4 cm:
v = (3 * 4) / (4 - 3) = 12 cm
Substituting v = 12 cm into the equation for dv/dt:
dv/dt = -(12^2) / 8
v/dt = -144 / 8
dv/dt = -18 cm/s
Therefore, the rate at which the v-distance is changing is -18 cm/s when u = 4 cm.
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What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent. a = 12%, b = 17% a = 12%, b = 18% a = 40%, b = 18% a = 41%, b = 63%
Answers
Answer:
The data that we have is:
Carrots = 84
Turnips = 25
Both = 17
Neither = 15
Root vegetables = 84 + 25 - 17 + 15 = 107
"a" is the percentage of carrots that also are turnips.
we know that 17 carrots are also turnips. so the relative frequency is:
17/107 = 0.158, in percent form this can be rounded to 16%.
b is the number of NOT carrots, that also are turnips.
This will be equal to the 25 turnips minus the 17 turnips that also are carrots
25 - 17 = 8
So we have 8 turnips that are not carrots.
Then we have:
b = 8/107 = 0.075
rounded to the nearest percent we get b = 8%.
So the values do not coincide with the options, and neither some of the data, for example the carrots that are not turnips are:
84 total carots, 17 of them are turnips, so we have 84 - 17 carrots that are not turnips:
84 - 17 = 67
then the relative frequency is:
P = 67/107 = 0.626, rounded to the nearest percent we get 63%
So there may be a number wrong in the diagram.
Answer:
B edg a=12% b=18%
Step-by-step explanation:
HURRY PLS 7TH GRADE MATH I NEED HELP I HAVE LESS THAN 5 MINS TO DO THIS
Answers
Answer:
35 = 8 + x + x + x + x + x +x
35 = 8 + 6x
6x + 8 = 35
35 - 8 = 6x
Step-by-step explanation:
hope this helps:)
Find the sum of -8x^2+3 and -9x^2+10x-10
Answers
Answer:
-17x² + 10x - 7
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
-8x² + 3 - 9x² + 10x - 10
Step 2: Simplify
Combine like terms (x²): -17x² + 3 + 10x - 10Combine like terms: -17x² + 10x - 7There are 6,00,000 shares of Rs. 100 each in a bank. Virochan has 1,580 shares in that bank. The bank makes a net profit of Rs. 40,00,00,000 in a year and it distributes 15% of the profit to the shareholders.
(a) Why is dividend different from bonus? Give reason.
(b) How much dividend did it distribute to all the employees? Find it.
(c) What percent of the total profit is distributed as dividend ?
Answers
a. Dividend is given to shareholder's while bonus are given from profit made in the revenue.
b. The shareholder's received a dividend of Rs. 10 per share
c. The bank shared 15% of it's profit.
Why is dividend different from bonus?(a) A dividend is a payment made to shareholders from a company's earnings. Employees may receive financial compensation in the form of bonuses in addition to their base pay. Bonuses are paid from a company's revenue, whereas dividends are paid from its profits. While bonuses are often given out on an annual basis, dividends are typically paid out weekly or annually. All stockholders receive dividend payments, however most employees only receive bonuses when they meet predetermined performance standards.
(b) The bank distributed 15% of its profit to the shareholders, which is equal to Rs. 6,00,00,000. This means that each shareholder received a dividend of Rs. 10 per share. Virochan has 1,580 shares, so he received a dividend of Rs. 15,800.
(c) The bank distributed 15% of its profit as dividend, which is equal to 15/100 = 0.15 = 15%.
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Ethan decides to type up some documents while waiting the meeting to start.He can type 2 pages every 1/8 hour.If the meeting started 3/4 hour later than the scheduled time,how many pages can he type before the meeting starts?
Answers
Answer: 4 pages
Step-by-step explanation:
To solve this problem, we need to use the formula:
Rate = Output/Time
Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.
Rate = 2 pages/(1/8 hour) = 16 pages/hour
Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.
Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages
Therefore, Ethan can type 4 pages before the meeting starts.
Answer: 4 pages
How does a real-world situation that is best described by a system of linear inequalities differ from a real-world situation that is best described by a single linear inequality?
Question content area bottom
Part 1
Choose the correct answer below.
A.
A real-world situation best described by a system of linear inequalities has multiple constraints. While a real-world situation best described by one linear inequality has only one constraint.
B.
A real-world situation best described by a system of linear inequalities has one constraint. While a real-world situation best described by one linear inequality has multiple constraints.
C.
A real-world situation best described by a system of linear inequalities has only one solution where the linear inequalities intersect. While a real-world situation best described by one linear inequality has infinitely many solutions which are located on the boundary line.
D.
A real-world situation best described by a system of linear inequalities has infinitely many solutions which are located on the boundary lines. While a real-world situation best described by one linear inequality has infinitely many solutions which are always just located in the shaded region.
Pls help me this is worth 20 points.
Answers
Answer:
either A. or D.
I'd say A. but don't take my word for it
Segment
A
B
‾
AB
has endpoints at
A
(
−
4
,
5
)
A(−4,5) and
B
(
12
,
13
)
.
B(12,13).
Determine the coordinates of point
C
C that lies on
A
B
‾
AB
such that
A
C
:
C
B
=
3
:
1
AC:CB=3:1
Answers
Answer:
12.5
Step-by-step explanation:
The hypotenuse of a right triangle measures 15 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearestytenth.
Answers
Answer:
14.5 cm
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
c = hypotenuse (15)
to solve for b (other leg), the equation is b^2 = c^2-a^2
15^2 - 4^2 = 209
\(\sqrt{209}\) = approx. 14.5
the other leg is (rounded to the nearest 10th) 14.5 cm
need a lil help please
Answers
Answer:
B(2, 4)Step-by-step explanation:
Given points:
A(-1, -9) and M(0.5, -2.5)Let the coordinates of B are (x, y)
Use midpoint formula to determine the point B:
0.5 = (- 1 + x)/2 ⇒ 1 = -1 + x ⇒ x = 1 + 1 = 2-2.5 = (-9 + y)/2 ⇒ -5 = -9 + y ⇒ y = -5 + 9 = 4