The 73rd term of the arithmetic sequence 18,30,42 = 882.
What is arithmetic sequence ?An arithmetic sequence seems to be a series of numbers that are ordered and share a common difference amongst each succeeding term. There are arithmetic sequences 3, 9, 15, 21, and 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
What does not constitute an arithmetic sequence?The sequence is not arithmetic if the difference between subsequent terms is not constant. Subtracting two consecutive elements from the sequence yields a common difference.
According to the given data:Let us now look for the explicit rule for with this arithmetic sequence. We have the following:
aₙ = a₁ + (n - 1) * d
= 18 + 12 * (n - 1)
= 12n + 6.
The 73rd term is 12 (73) + 6 = 882.
The 73rd term of the arithmetic sequence 18,30,42 = 882.
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Suppose g ( x ) = √ x − 3 / x − 11 . what is the domain of g?
The domain of the function g ( x ) = √ x − 3 / x − 11 is R - 11.
What does a function's domain entail?Inputs are assigned outputs by functions. The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
How do you determine a function's domain?Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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132891 rounded to the nearest thousand is?
Answer:
132, 900.
Step-by-step explanation:
The 9 is in the tens, so it tells the hundreds to go up by 1 to 9 & add 2 zero's beside. The answer would be 132, 900.
Helppppp! Line A and Line B are parallel and Line P is a transversal. The measure of angle 3 is 52°.
Find the measures of the rest of the angles in the diagram.
Answer:
Angle 1: 28 degrees
Angle 2: 52 degrees
Angle 3: 52 degrees
Angle 4: 28degrees
Angle 5: 28degrees
Angle 6 : 52degrees
Angle 7 : 52degrees
Angle 8 : 28degrees
Graph the image of △RST after a reflection over the line y=x.
Answer:
Put S=(1,-10) R(-10,-8) T(-8,-9) Make sure to put a ´ after these letters when you put them down
Step-by-step explanation:
What ia the answer for 4.5 gl to dl
Answer: 45,000,000,000 dl
Step-by-step explanation:
10,000,000,000 dl=1 gl
4.5 gl * 10,000,000,000 dl/1 gl =
4.5 * 10,000,000,000 dl = 45,000,000,000 dl
Given the recursive formula shown, what are the first 4 terms of the sequence?
f(n)=
f(1) = 3
(f(n)=f(n-1)+4 if n>1
OA) 3, 7, 11, 15
B) 4, 7, 10, 13
C) 3, 9, 11, 13
D) 3, 8, 10, 12
Answer:
Option A: 3, 7, 11, 15
Step-by-step explanation:
f(2) = f(1) + 4 = 3 + 4 = 7
f(3) = f(2) + 4 = 7 + 4 = 11
f(4) = f(3) + 4 = 11 + 4 = 15
f(5) = f(4) + 4 = 15 + 4 = 19
I do not remember how to solve this
Answer:
Your answer is correct
Step-by-step explanation:
Use the rules of exponents to simplify the expression.
(q⁶)²To raise a power to another power, multiply the exponents.
q⁶ˣ²Multiply 6 by 2.
q¹²The correct option is the third.
Skandarcan someone help me with this
Step-by-step explanation:
so it starts with
182 = 182 × 3 / p
as the price is inversely related to D.
(a)
so, in general
D = 182 × 3/p = 546/p
(b)
D = 546/3.25 = 168 bags
if the price increases to $3.25, then they will sell only 168 bags.
I am sure, the function will not stay linear for every value of p. for example, if they increase the price to $546 per bag, they would still sell 1 bag. but I am certain, they would fall to 0 sold bags much, much earlier than that ...
4
Albert made $54.25 bagging groceries for 5 hours last week. What was Albert's hourly wage? '
Answer:
$10.85
Step-by-step explanation:
Divide 54.25 by 5 and you get 10.85.
Solve for x can you help set up the problem for me to solve for x I have tried everything
As per the alternate angle property, alternate angles are equal hence, is x = 7.
What is the alternate angle property?
The alternate angle theorem states that when two resemblant lines are cut by a transversal, also the performing alternate interior angles or alternate surface angles are harmonious. To prove If two resemblant lines are cut by a transversal, also the alternate innards angles are equal. The Alternate Exterior Angles Theorem states that, when two resemblant lines are cut by a transversal, the performing alternate surface angles are harmonious. Then, the two angles of c and d are outside of the resemblant lines and so these are two exemplifications of alternate surface angles.Equating the alternate angles,
11x-2=10x+5,
11x - 10x = 5 + 2
x = 7
Since, as per the alternate angle property, alternate angles are equal.
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C=-
Convert the following temperatures from Fahrenheit to Celsius or vice versa.
F - 32
1.8
a. 50°F
F = 1.8C +32
b. 75°C
C. -40°C
Answer:
A)50°F = 10°C
B)75°C = 167°F
C)-40°C = -40°F
Step-by-step explanation:
A) 50°F = 10°C
Formula
(50°F − 32) × 5/9 = 10°C
B) 75°C = 167°F
Formula
(75°C × 9/5) + 32 = 167°F
C) -40°C = -40°F
Formula
(-40°C × 9/5) + 32 = -40°F
A shopkeeper allows a discount of 10% on the marked price of an article.What was the marked price of the article which costs him 1800 and makes profit of 15%.
Answer:
$243 is his profit
Step-by-step explanation:
Answer: $4100
Step-by-step explanation:
discount = [tex]\frac{1800}{90}[/tex]×100 = 2000
profit = [tex]\frac{115}{100}[/tex]×2000 = 2300
market price = 2300 + 1800 = 4100
This is a conversion graph between litres and gallons. Use the graph to convert 60 gallons to litres
Disclaimer: The conversion graph is missing in the question.
60 gallons is equal to 227.125 litres.
Refer to the attached image for the conversion of litres to gallons.
And gallons to litres.
In this image, a vertical line is drawn from the given value of gallon until it meets the cross line. And then a horizontal line is drawn, which touches the litres line.
At the point at which this horizontal line touches the litres line, that value is considered as the corresponding litres for the given gallons.
Similarly, a vertical line is drawn from the litres line until it meets the cross line. And then a vertical line is drawn, which touches the gallons line.
At the point at which this vertical line touches the gallons line, that value is considered as the corresponding gallons for the given litres.
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Determine the following ratio
Using relations in a right triangle, the secant of angle θ is given by:
D. 5/4.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:
h² = 9² + 12²
h = sqrt(9² + 12²)
h = 15.
The secant of an angle is 1 divided by the cosine, hence:
cos(θ) = 12/15 = 4/5.sec(θ) = 5/4.Which means that option D is correct.
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A spinning disk with radius 10 cm rotates at 120 rpm.
1. Find the angular speed:
2. Find the linear speed of a point on the edge of the disk:
1) The angular speed is approximately 12.566 radians per second.
2) The linear speed of a point on the edge of the disk is 1.257 meters per second.
What are the angular speed and the linear speed of a spinning disk?
1) Herein we have a disk that spins at constant angular speed (ω), in radians per second, whose magnitude is found dimensional analysis and unit conversions:
ω = 120 rev / min × (2π rad / 1 rev) × (1 min / 60 s)
ω ≈ 12.566 rad / s
The angular speed is approximately 12.566 radians per second.
2) The linear speed (v), in meters per second, on the edge of the disk is described by the following formula:
v = R · ω
Where R is the radius of the spinning disk, in meters.
If we know that R = 0.1 m and ω ≈ 12.566 rad / s, then the linear speed is:
v = (0.1 m) · (12.566 rad / s)
v = 1.257 m / s
The linear speed of a point on the edge of the disk is 1.257 meters per second.
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How many kg of peanuts must Heather
add to 4 kg of mixed nuts containing 60%
peanuts to make a mixture with 92%
peanuts?
37.375 kg of peanuts must be added to the 4 kg of mixed nuts to make a mixture containing 92 % of peanuts.
Total mixture of mixed nuts = 4 kg
60 % of them are peanuts.
So, we will calculate the percentage:
Let x be the amount of peanuts.
60 / 100 x = 4 kg
0.6 x = 4 kg
x = 4 kg / 0.6
x = 6.67 kg
Now let the peanuts added be y
So, 92 % of ( 4 kg + y ) should be peanuts.
So, we get the equation as:
0.92 ( 4 ) + 0.92 y = 6.67 + y
3.68 + 0.92 y = 6.67 + y
0.08 y = 2.99
y = 37.375 kg
Therefore, 37.375 kg of peanuts must be added to the 4 kg of mixed nuts to make a mixture containing 92 % of peanuts.
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Please help!
Simplify:
Step-by-step explanation:
[tex] = ( \frac{3}{5} {)}^{2} [/tex]
[tex] = \frac{ {3}^{2} = 3 × 3 }{ {5}^{2} = 5 × 5 } \\ [/tex]
[tex] = \frac{9}{25} \\ [/tex]
☘️☘️☘️...
Answer:
[tex] \frac{9}{25} [/tex]
Step-by-step explanation:
[tex] { ( \frac{3}{5} )}^{2} \\ = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ = \frac{9}{25} [/tex]
Divide. Please help 10 points.
Answer:
The answer to the question is the third answer
22.83/0.06 = __________
Answer: 380.5
Step-by-step explanation: you can type it into desmos graphing calculator
Find the square root of: 2 + sqrt5
Answer:
3.65
Step-by-step explanation:
The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6
To two decimal places,
√70
must lie between ____
and _____.
To two decimal places ✓70 just be between 8.36 and 8.37.
How to illustrate the information?It should be noted that we simply have to calculate the information is to find the square root of 70.
Therefore, this is approximately 8.366
Therefore, to two decimal places ✓70 just be between 8.36 and 8.37.
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.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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Solve the equation.
-2= 6/7p p=?
Answer: P= 2 6/7
Step-by-step explanation:
Pls help show work pamdas
Answer:
Answer is -4
Step-by-step explanation:
To solve this, you want to substitute the values of x and y. So, 2(-3)^2-5(-3)(-2)-(-2)^3 which will give you -4.
In Fairbanks the temperature went down 20 degrees in 6 hours
Answer: 3.3 hours
Step-by-step explanation:
the peremiter of a parallelogram is 56 meters The width of the parallelogram is 4 meters less than its length find the length and the width of the parallelogram
The length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
We are given that the perimeter of a parallelogram is 56 m.
Let the length of the parallelogram be x meter.
So, we get that the width of the parallelogram will be = x - 4 meter.
We also know that:
Perimeter of parallelogram = 2 ( l + b )
Substituting the values in this, we get that:
56 = 2 ( x + x - 4 )
56 = 2 ( 2 x - 4 )
28 = 2 x - 4
2 x - 4 = 28
2 x = 28 + 4
2 x = 32
x = 16
Length = 16 m
Width = 16 - 4 = 12 m
Therefore, the length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
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5. A population with mean = 37 and standard deviation = 6 is standardized so that the new mean is 50 and the new standard deviation is 10. A scale of 40 on the first scale is equivalent to what score on the new standardized scale?
Using z-scores, it is found that a scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.
What are z-scores?The z-score of a measure X of a distribution with mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. Looking at the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For the first scale, the parameters are given as follows:
[tex]X = 40, \mu = 37, \sigma = 6[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (40 - 37)/6
Z = 0.5.
For the second scale, we want to find X when Z = 0.5, considering the following mean and standard deviation:
[tex]\mu = 50, \sigma = 10[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.5 = (X - 50)/10
X - 50 = 5
X = 55.
A scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.
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Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
A line passes through point 6, 1 and has a slope of 43. Write an equation in =+AxByC form for this line. Use integers for A, B, and C.
Answer:
4x-3y=21.
Step-by-step explanation:
1) the common view of slope-interception form is y=slope*x+interception;
2) if according to the condition the slope=4/3, then the required equation is
[tex]y=\frac{4}{3}x +interception;[/tex]
3) in order to calculate the interception it is enough to substitute the given coordinates into this equation:
[tex]1=6*\frac{4}{3} +interception; \ = > \ interception=-7;[/tex]
4) the slope interception form of the required equation is:
[tex]y=\frac{4}{3}x-7;[/tex]
5) if to re-write the equation in slope-interception form into the required, then (A=4; B=-3; C=21):
4x-3y=21.
Let S be the universal set, where:
S = {1, 2, 3, ..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Set A = {7, 9, 12, 13, 14}
Set B =
{1, 4, 5, 7, 16, 18, 19}
Set C= {4, 6, 8, 9, 11, 13, 15, 16, 17, 19}
LIST the elements in the set (AUBUC)
(AUBUC) = {
-Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
LIST the elements in the set (An BnC)
(An BnC) = {
}
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
You may want to draw a Venn Diagram to help answer this question.
The elements of (A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
The elements of (A∩B∩C) = DNE
SetsFrom the question, we are to list the elements of the given sets
From the given information,
Set A = {7, 9, 12, 13, 14}
Set B = {1, 4, 5, 7, 16, 18, 19}
Set C = {4, 6, 8, 9, 11, 13, 15, 16, 17, 19}
We are to list the elements of (A∪B∪C)
(A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
Also, we are to list the elements of (A∩B∩C)
(A∩B∩C) = { } OR ∅
Since this is an empty set
(A∩B∩C) = DNE
Hence,
The elements of (A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
The elements of (A∩B∩C) = DNE
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