261 , 256 , 251 Find the 50th term
Answers
then, for all n greater or equal than 1
\(f(n)=261-5n\)then the 50th term is f(49)= 261-5(49)= 16, then the final answer is 16.Related Questions
please help with question
Answers
The solution is Option A.
The value of the equation is g ( x - 3 ) = √ ( x - 12 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as g ( x )
Now , the value of g ( x ) is
Substituting the values in the equation , we get
g ( x ) = √ ( x - 9 ) be equation (1)
On simplifying the equation , we get
when the value of x is x - 3 , we get
g ( x - 3 ) = √ ( x - 3 ) - 9
On further simplification , we get
g ( x - 3 ) = √ ( x - 3 - 9 )
g ( x - 3 ) = √ ( x - 12 )
Hence , the equation is g ( x - 3 ) = √ ( x - 12 )
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the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
Answers
Answer:
470.4 mm
Step-by-step explanation:
Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.
First, find 12% of 420 mm:
12% of 420 mm
\(\frac{12}{100}\) x 420 mm
1.2 x 420 mm
= 50.4 mm
Then add 50.4 mm to the previous annual rainfall of 420 mm:
50.4 mm + 420 mm
= 470.4 mm
Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.
Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Answers
= 173.903t
Step-by-step Explanation:
The given equation is: f(t) = 227e^(b*t)
To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.
Let's start by taking the natural logarithm (ln) of both sides:
ln(f(t)) = ln(227e^(b*t))
Using the properties of logarithms, we can simplify this to:
ln(f(t)) = ln(227) + ln(e^(b*t))
ln(f(t)) = ln(227) + b*t
Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:
ln(f(t)) = ln(a) + k*t
where a = 227 and k = -0.09
Taking the exponential of both sides, we get:
f(t) = e^(ln(a) + k*t)
f(t) = e^(ln(a)) * e^(k*t)
f(t) = a * e^(k*t)
Substituting the values of a and k, we get:
f(t) = 227 * e^(-0.09*t)
Therefore, the equation f(t) = ab is:
f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)
Is 45+12.5x greater than less than or equal to 75+7.5x
Answers
Answer:
\(45+12.5x < 75+7.5x\)
Step-by-step explanation:
set each problem to 0 and solve.
Take the answer and plug it in for x. the 1st problem is less than the 2nd.
Need help placing in correct spot
Answers
The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.
Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.
Hence,
∠3 = 180 - 62 = 118 degrees(angles on a straight line)
∠1 ≅ ∠3 (vertically opposite angles)
∠7 ≅ ∠3 (alternate interior angles)
∠5 ≅ ∠7 (vertically opposite angles)
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Solve (x-3)^2-2=x+1 graphically
Answers
Answer:
Step-by-step explanation:
To solve the equation graphically, we need to first rearrange it into the form of y = f(x). So, let's simplify the given equation:
(x - 3)² - 2 = x + 1
Expanding the left side:
x² - 6x + 9 - 2 = x + 1
Simplifying:
x² - 7x + 6 = 0
Now we can graph the function y = f(x) = x² - 7x + 6 and the line y = x + 1 on the same coordinate axes and find their intersection points.
Here's a graph of the function and the line:
Graph of y=x^2-7x+6 and y=x+1
We can see that the two curves intersect at two points, which have x-coordinates of approximately 1.2 and 5.8. So, the solutions to the equation are x ≈ 1.2 and x ≈ 5.8.
Kayla is thinking of a 3-digit number.
* It is divisible by 18.
* It is a palindrome (It reads the same left-to-right as it does right-to-left, like 252 and 848).
* It is one less than a multiple of 5.
What is Kayla’s number?
Answers
Answer:
kaylas thinking of the number 414
Step-by-step explanation:
414 is divisable by 18 (414 divided by 23)
414 is palindrome
414 is one less than a multiple of 5 (415)
Answer:
414
Step-by-step explanation:
The last digit must be 4 or 9 since it is one less than a multiple of five. Then, it says the number must be divisible by 18, and 18 = 2x9. Only 4 is divisible by 2, so four must be the last digit. Since it's a palindrome, the first digit must also be four. Since it also has to be divisible by nine, 4 + 4 = 8, and 8 + 1 = 9.
K
The perimeter of a rectangular sports court is 148 feet. After a game, a player's coach estimates that the athlete has run
a total of 353 feet, which is equivalent to four times the court's length plus seven times its width. What are the
dimensions of the sports court?
The length is
feet.
Answers
Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.
And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.
We can use these two equations to find the dimensions of the court. Solving the first equation for W:
W = (148 - 2 * L) / 2.
Substituting this expression for W into the second equation:
4 * L + 7 * (148 - 2 * L) / 2 = 353
Expanding and simplifying the right side of the equation:
4 * L + 74 - 7 * L = 353
-3 * L = -279
L = 93 feet.
Finally, using the expression for W from the first equation:
W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.
So the dimensions of the sports court are 93 feet by 32 feet.
Step-by-step explanation:
if your gross pay is 2190. How much of your gross pay wull be deducted for FICA TAXES
Answers
The amount of your pay that will be deducted for FICA Taxes is given as follows:
187.25.
How to obtain the deducted amount?The amount of your pay that will be deducted for FICA Taxes is obtained applying the proportions in the context of the problem.
The FICA tax rates are given as follows:
Social Security tax rate: 6.2% for both employees and employers on wages up to $142,800. This means that both employees and employers contribute 6.2% of an employee's wages up to $142,800 to fund Social Security.Medicare tax rate: 1.45% for both employees and employers on all wages earned. This means that both employees and employers contribute 1.45% of an employee's wages to fund Medicare.Additional Medicare tax: 0.9% for employees earning more than $200,000 annually. This additional tax is only paid by employees and not by employers.Hence the total rate is given as follows:
6.2 + 1.45 + 0.9 = 8.55.
Hence, out of a gross pay of 2190, the deduction is given as follows:
0.0855 x 2190 = 187.25.
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Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec θ sec 0 in simplest form with a rational denominator?
Answers
Answer:
\(\sqrt{2}\)
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
\(\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}\)
Now, secant is the inverse of cosine.
Therefore:
\(\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}\)
See whether you're understanding the subject and skills.
Answers
If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training
As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.
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.
A train leaves at 15:43 and arrives at 17:13. It travelled at an average speed of 75 km/h.
How far did it travel? Give your answer in km to 1DP.
Can anyone answer this
Answers
Answer:
Distance cover by train = 112.5 km
Step-by-step explanation:
Given;
Speed of train = 75 km/h
Time started = 15:43 min
Time ended = 17:13 min
Find:
Distance cover by train
Computation:
Time started = 15:43 min = 15.716 hour
Time ended = 17:13 min = 17.216 hour
Total time taken = 17.216 - 15.716
Total time taken = 1.5 hour
Distance cover by train = Total time taken x Speed of train
Distance cover by train = 75 x 1.5
Distance cover by train = 112.5 km
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the appe slices. So he conducted a study where he used a peanut butten oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different votes
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis
a. There food preferences among vole species are independent of one another.
b. There is a relationship between voles and food preference.
c. To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected
meadow voles common voles
apple slices 15 21
peanut butter-oatmeal 25 16
Answers
Answer:
Throughout the clarification category elsewhere here, the definition of the concern is mentioned.
Step-by-step explanation:
Null hypothesisThere seems to be no option for consuming peanut butter oatmeal mixture including apple slices with Meadow voles as well as regular voles.
Alternative hypothesisMeadow voles tend to consume a combination of peanut butter oatmeal whereas different or specific votes prefer eating slices of apples.
HELP PLEASE I NEED ANSWER NOW
Answers
Answer:B
Step-by-step explanation:
I think it should be B u= -1
the bag of letter tiles include 15 vowels and 25 consonants. What is the probability of selecting two vowels one after another NEED HELP ASAP
Answers
Answer: 0.1346
Step-by-step explanation:
Number of vowels = 5 vowels
Number of consonants = 25
For us to calculate the probability of selecting two vowels one after another, we have to select the first vowels which will give a probability of 5/40, then we select the second vowel which will be 4/24 since there'll be 4 vowels left 39 alpahabets.
Therefore, probability of selecting two vowels one after another will be:
= 15/40 × 14/39
= 3/8 × 14/39
= 0.1346
Solve the triangle.
A= 108° C=27° c = 160
Answers
if angle A is 108 degrees, angle B is 27 degrees then angle C is 45 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that angle A is 108 degrees
Angle B is 27 degrees
We need to find angle C
By angle sum property we know that the sum of three angles is 180 degrees
108+27+x=180
135+x=180
Subtract 135 from both sides
x=180-135
x=45 degrees
Hence, if angle A is 108 degrees, angle B is 27 degrees then angle C is 45 degrees.
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In a triangle ABC, Find the angle C when angle A= 108° ,B=27° .
Can you help me please
Answers
Answer:
this is the ans
Step-by-step explanation:
hope it helps!!!
in the form, y=a(1+r)^t PLEASEEEEEE
Answers
Answer:
y
a= ——
(r + 1 )t
Step-by-step explanation:
divide both sides
pls help me with this problem :)
The areas of two similar triangles are 9 cm² and 49 cm². One of the sides of the first
triangle is 2 cm. What is the length of the corresponding side of the other triangle?
Answers
Answer:
I believe it should be rounded to 11, if not decimal would be 10.88
Step-by-step explanation:
49 divided by 9 equals 5.44 which is the amount times the 49cm^2 triangle is compared to the 9cm^2. So then the side is 2cm, multiply by the amount times bigger the other triangle is which would be 10.88. Hopefully I'm not wrong:)
Answer:
The answer is 4 and 2/3 cm²
Step-by-step explanation:
Take the square root of 49 and 9 and you'll get 7 and 3 since the scale factor is the large area over the small area.
The large area would be √49 cm²
The small area would be √9 cm²
7 x cm
------ = ----------, cross multiply
3 2 cm
7 × 2 = 3 × x
14 = 3x
x = 14/3, x = 4 and 2/3
The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.482, 1.614, and 0.295, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Yes the test suggest that the true average percentage of organic matter in such soil is something other than 3%
Step-by-step explanation:
From the question we are told that
The sample mean is \(\= x = 2.482\%\)
The standard deviation is \(\sigma = 1.614\)
The standard error is \(SE = 0.295\)
The sample size is \(n = 30\)
The level of significance is \(\alpha = 0.05\)
The null hypothesis is \(H_o : \mu = 3\%\)
The alternative hypothesis is \(H_a : \mu \ne 3\%\)
Now the degree of freedom is evaluated as
\(df = n - 1\)
\(df = 30 - 1\)
\(df = 29\)
The test statistics is mathematically evaluated as
\(t = \frac{ 2.482 - 3}{ 0.295}\)
\(t = -1.756\)
The p-value is obtained from the the student t -distribution table , the value is
\(p-value = P( T \le t)= 2 * t_{ t, df } = t_{ -1.756 , 29 } = 2 *0.0448= 0.0896\)
The reason for the 2 in the equation is because the test is a two -tailed test i.e -1.756 and 1.756
Given that the \(p-value > \alpha\) then we fail to reject the null hypothesis
Hence the test the suggest that the true average percentage of organic matter in such soil is something other than 3%
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
Use the quadratic formula, which states that x = [-b ± √(b^2 - 4ac)] / 2a, where a, b, and c are the coefficients of the quadratic equation.
Substitute the values of a, b, and c into the formula and simplify to get the values of x.
Factor the quadratic equation by finding two numbers that multiply to give ac (in this case, -6) and add to give b (in this case, 12). Use these numbers to rewrite the quadratic equation as (2x - 1)(x + 3) = 0 and solve for x.
Therefore, the options given do not correctly represent the steps to solve the quadratic equation.
Find the measures of each numbered angle
Answers
help please. is due today. Thank you.
Answers
damp everyone is giving exams lol
Answer:
Step-by-step explanation:
take 22 degree as reference angle
using cos rule
cos 22=adjacent/hypotenuse
0.92=56/x
x=56/0.92
x=60.86
x=60.9
write each info entire radical √48
Answers
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
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order the number least to greatest 3 2/3, 362%, 3.66, 36
Answers
Answer:
362%, 3.66, 3 2/3, 36
Step-by-step explanation:
Answer: 362%, 3.66, 3 2/3, 36
I hope this helps!
Hi! please click the image, its one of my homework problems and it would be helpful if someone could help me work through it.
Answers
The linear velocity of a point on the equator is 1047.2 miles per hour.
The angular speed of a point on Earth is π/12 radians per hour. The equator lies on a circle whose radius is approximately 4000 miles. We need to find the linear velocity in miles per hour. The linear velocity is the product of the radius and the angular speed.
In physics, angular velocity, often known as rotational velocity, is a pseudovector representation of how quickly an object's angular position or orientation varies with time. Linear velocity is the rate of change of displacement in relation to time when an item travels along a straight line.
v = rω = 4000*π/12 = 1047.2 miles per hour
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3x-5 (2x+6) = 4(2x+3)+18
Answers
Answer:
= − 4
Step-by-step explanation:
what is y equals 5 times x equal
Answers
Answer:
multiple possibilities
Step-by-step explanation:
Y=5x
yx=5
it is unsolvable but have various possible answers:
y=5
x=1
(vise versa)
————
y=2.5
x=2
(vise versa)
x = ?????????????????
Answers
Answer:
4
Step-by-step explanation:
m thanks for th help
Answers
Step-by-step explanation:
here's the answer to your question
Since this is a right triangle, we can use trigonometry. We will use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking at angle V, we know the opposite side and the adjacent side. Therefore, we should use the tangent function.
tan(V) = 3/6
To solve, use the inverse tangent function (tan^-1) on your calculator.
V = 26.6 degrees
Hope this helps!