This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by
1
3
gives the next term. In other words,
a
n
=
a
1
r
n
−
1
.
Geometric Sequence:
r
=
1
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
486
and
r
=
1
3
.
a
n
=
486
(
1
3
)
n
−
1
Apply the product rule to
1
3
.
a
n
=
486
1
n
−
1
3
n
−
1
One to any power is one.
a
n
=
486
1
3
n
−
1
Combine
486
and
1
3
n
−
1
.
a
n
=
486
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
5
=
486
3
(
5
)
−
1
Simplify the denominator.
Tap for more steps...
a
5
=
486
81
Divide
486
by
81
.
a
5
=
6
PLEASE HELP
50 POINTS
Answer:
9. [tex]256u^8 v^{16}[/tex]
10. [tex]-32x^{10} y^{35}[/tex]
11. [tex]-x^{12}y^{20}[/tex]
12. 1
13. [tex]\frac{2}{3xy^3}[/tex]
14. [tex]\frac{h^8}{3j^6k^6}[/tex]
15. [tex]\frac{1}{4z}[/tex]
Answer:
9. 256u^8 v^16
10. -32x^10 y^35
11. x^12 y^21
12. 1
Step-by-step explanation:
If you can, please give me a Brainliest; thank you! I put a lot fo times to solve it !
4. The density of gold is 18 g/cm3. If the volume of a plece of gold is 13cm, how many grams will it be?
ANSWER:
Therefore there are about 234 grams
STEP-BY-STEP EXPLANATION:
We have that the density is given by this formula
[tex]\begin{gathered} d=\frac{m}{V} \\ \text{where m is the mass and V the volume} \end{gathered}[/tex]We have the value of the density and the volume, therefore we can calculate the number of grams as follows:
[tex]\begin{gathered} 18=\frac{m}{13} \\ m=18\cdot13 \\ m=234 \end{gathered}[/tex]I haven’t came across one of these questions so not sure how to solve
m∠F = 140º
1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:
[tex]\begin{gathered} S_i=180(n-2) \\ S_i=180(4-2) \\ S_i=180(2) \\ S_i=360 \end{gathered}[/tex]Note that "n" refers to the number of sides:
Notice also that angle H is a right angle since this is not an Isosceles Trapezoid
So we can write out the following
9x +14x +4x + 90 = 360º
27x = 360 -90
27x = 270
x =10
Alternatively, angles between parallel lines are supplementary
2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:
m∠F = 14x
m∠F = 140º
Two observers are standing on shore 20 mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. one observer is 10 miles from the sailboat and the other observer is 25 miles from the sailboat. round to the nearest degree
Using the law of sines, supposing C = 30º, the angle of each observer with the sailboat is:
Observer A: 136º.Observer B: 14º.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A has length a.The length of the side opposite to angle B has length b.The length of the side opposite to angle C has length c.The lengths and the sine of the angles are related according to the following rule:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The measure of angle B is found as follows:
sin(B)/10 = sin(C)/20
sin(B)/10 = 0.5/20 (sin(C) = 0.5)
sin(B) = 5/20
sin(B) = 0.25
B = arcsin(0.25)
B = 14º.
The measure of angle A is found as follows:
sin(A)/25 = sin(C)/20
sin(A)/25 = 0.5/20 (sin(C) = 0.5)
sin(A) = 12.5/20
sin(A) = 0.625
A = arcsin(0.625)
A = 136º.
Missing informationThe problem is incomplete, hence we suppose that the angle C is of 30º and problem asks for the angle measure of each angle.
(drawing is not to scale).
More can be learned about the law of sines at https://brainly.com/question/4372174
#SPJ1
Dilate this figure by a scale factor of 1.5. Is the image a stretch or compression?
Answer:
compression
Step-by-step explanation:
If b>1 then the graph will compress
Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?
Answer:
The three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
Explanation:
Given the base and height pairs in the question.
Let us use the corresponding pairs that gives the same area.
Firstly, for the first pair;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times10\times7=35cm^2 \\ A=\frac{1}{2}\times10\times2.5=12.5cm^2 \end{gathered}[/tex]Secondly, the second pair is;
[tex]\begin{gathered} A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times5\times3.5=8.75cm^2 \\ A=\frac{1}{2}\times5\times2.5=6.25cm^2 \end{gathered}[/tex]Thirdly, the third pair;
[tex]\begin{gathered} A=\frac{1}{2}\times14\times3.5=24.5cm^2 \\ A=\frac{1}{2}\times14\times7=49cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]Therefore, the three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
when 9 times a number is increased by 30, the answer is the same as when 140 is decreased by the number. Find this number
Answer: 11
Step-by-step explanation:
Let the number be x.
[tex]9x+30=140-x\\\\10x=110\\\\x=11[/tex]
The drivers at a warehouse need to deliver 40,000 packages each day. The warehouse has 128 trucks. Each truck has 350 packages. The drivers deliver all the packages on the trucks. Do the warehouse drivers deliver enough packages
Yes. The warehouse drivers deliver enough packages.
What is an expression?An expression is used to illustrate the information that's given.
In this case, the warehouse has 128 trucks. Each truck has 350 packages. The number of packages that van be delivered will be:
= Number of trucks × Amount in each package
= 128 × 350
= 44800
Since the drivers at a warehouse need to deliver 40,000 packages each day. this means they denied enough packages because 44800 is more than 40000.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
A flagpole cast a shadow that is 15 feet long. The angle of elevation at this time is 40 degrees . How tall is the flag pole?
Flag pole is 12585 feet long.
Define Tangent.The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together. A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve.
Given Data
Angle of elevation = 40°
Adjacent = 15 feet
Let height of opposite be x
tan(A) = [tex]\frac{opposite}{adjacent}[/tex]
tan(A) = [tex]\frac{x}{15}[/tex]
x = 15tan(40)
x = 15(0.839)
x = 12,585
Flag pole is 12585 feet long.
To learn more about tangent, visit:
https://brainly.com/question/19064965
#SPJ13
Robert gets a loan from the bank. agrees to borrow 6000 , his interest rate is 7 %. he agrees to pay back over a 10 year period. how much money wil he have paid back by then?
The amount to be paid after paying interest of 7% for 10 years is 10,2000
The amount to be borrowed from the bank = 6000
Interest rate for the amount per year = 7%
The total time period of the loan = 10 years
Thus , the final amount can be calculated by using the formula
A = P(1 + rt)
where A is the final amount
P is the principal amount to be borrowed
r is the rate of interest
t is the time period
Now, let us substitute the known values in the above equation , we get
A = 6000 ( 1 + 0.07 x 10)
= 6000 (1 + 0.7)
= 6000 (1.7)
A = 10,200
Therefore , the final amount to be paid is 10,200
Learn more about the simple interest in
https://brainly.com/question/25845758
#SPJ4
2x^2-5x-11=1
factor pls
Answer:
(2x+3)(x-4) = 0
Step-by-step explanation:
Suppose that 13 inches of wire costs 52 cents.
At the same rate, how many inches of wire can be bought for 36 cents?
Answer:
9 inches
Step-by-step explanation:
Set it up like a fraction ratio and solve for x. as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.
[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]
13*36 = 468
468/52 = 9
Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.
The stock price for JSR was $74.29 in August. In September the stock had increased by 7%, but in October the price fell by 7%. What was the price of JSR stock in October? Round your answer to the nearest cent, if necessary.
In order to find the price increase multiply by 1 and add the 7%,
[tex]\begin{gathered} 74.29\cdot(1+0.07) \\ 74.29\cdot1.07 \\ 79.4903 \end{gathered}[/tex]then, apply the same to subtract the 7%
[tex]\begin{gathered} 79.4903\cdot(1-0.07) \\ 79.4903\cdot(0.93) \\ 73.925\approx73.93 \end{gathered}[/tex]4 2/15 / 3.1 (I NEED HELP NOW!!!!!!!!!!!)
Answer:
The answer would be 1.3, and the three is repeating.
Step-by-step explanation:
First, make 4 2/15 into a improper fraction.
4 2/15= 62/15
Now, when we divide fraction, use the rule Keep, Change, Flip.
Keep the 62/15.
Change the division sign into a multiplication sign.
To make the 3.1 into a fraction, put a one over it.
3.1/1
Now, flip the fraction.
3.1/1= 1/3.1
Your equation will look like this:
62/15x1/3.1
Multiply across.
62/46.5
Now simplify.
The answer would be 1.3, and the three is repeating.
A magical basket of pennies doubles every day. If the basket if full on the 15th day, on what day was the basket one-quarter full?
The basket of pennies will be 1/4 full on the 13th day
How to determine the day?From the question, the given parameters are:
Rate of change, r = 2 i.e. doubleFull basket, = 15th dayThe above parameters illustrate an exponential function
An exponential function is represented as
A(n) = A * (r)ⁿ⁻¹
Where
A represents the initial value
It is full on the 15th day
So, we have
1 = A *(2)¹⁵⁻¹
Evaluate
1 = A *(2)¹⁴
Divide by (2)¹⁴
A = (2)⁻¹⁴
Substitute A = (2)⁻¹⁴ in A(n) = A * (r)ⁿ⁻¹
A(n) = (2)⁻¹⁴ * (2)ⁿ⁻¹
When it is one-quarter full, we have
1/4 = (2)⁻¹⁴ * (2)ⁿ⁻¹
Multiply by (2)¹⁴
(2)¹² = (2)ⁿ⁻¹
By comparison, we have
n - 1 = 12
Add 1 to both sides
n = 13
Hence, the basket will be one-quarter full on the 13th day
Read more about exponential function at
https://brainly.com/question/11464095
#SPJ1
Simplify the expression.
2/5y−4+7−9/10y =
Answer:
[tex]\frac{1}{2}[/tex] y +3
Step-by-step explanation:
You want to combine like terms
[tex]\frac{2}{5}[/tex] y and [tex]\frac{-9}{10}[/tex] y are like terms because they both have a variable y
-4 and + 7 are like terms because they are both constants. (numbers without letters)
We combine these
[tex]\frac{4}{10}[/tex] means the same as [tex]\frac{2}{5}[/tex] I just multiplied the numerator (top) and the denominator (bottom) by 2. I did this so that I could add it to [tex]\frac{-9}{10}[/tex]
[tex]\frac{4}{10}[/tex]y - [tex]\frac{9}{10}[/tex]y = [tex]\frac{-5}{10}[/tex] y (4-9 = -5) or [tex]\frac{-1}{2}[/tex] y simplified
-4 + 7 = 3
-0.5f - 4.52 = -25.52 + f HELP PLEASE
Answer:
-0.5f - 4.52 = -25.52 + 1f
-1.5f = 21
f = 14
Answer:
14
Step-by-step explanation:
-4.52 + 25.52 = f + 0.5f
21 = 1.5f
f = 14
Can someone help me, please? its timed
The measure of the lableled angles are x = 202 and (x - 44) = 158
What are the values of the labeled angles?Before we can solve this question, we need to understand the geometry of the shape.
The shape we have here is a pentagon. The sum of angles in a pentagon is 540. The angle with a red square is a right angle and the value is 90.
Therefore:
x + 90 + 90 + (x - 44) = 540
x + 180 + x - 44 = 540
2x + 136 = 540
2x = 540 - 136
2x = 404
x = 404/2
x = 202
Also:
(x - 44) = 202 - 44 = 158
Therefore, the angles x and (x - 44) measure 202 and 158 respectively.
Learn more about geometry on:
https://brainly.com/question/11435541
#SPJ1
The unknown value x in the polygon is equal to 112 degrees.
Sum of Angles in a PolygonThe sum of angles in the given polygon be equal to 360 degrees. This implies that when we add all the total sides together, we must have a total of 360 degrees.
Since one of the indicated sides is a right angle, we can sum everything up and solve for x
Mathematically;
[tex]90 + 90 + x +(x - 44) = 360[/tex]
Solving the equation above;
[tex]180 + x + x - 44 = 360\\180 + 2x - 44 = 360\\x = 112[/tex]
The value of x in the figure given is 112.
Learn more on angle in a polygon here;
https://brainly.com/question/1592456
#SPJ1
Round 3.44570830811 to the nearest hundred-thousandth
Answer:
3.44571
Step by step explanation:
3.44570830811
8 is the number next to the place value of hundred-thousandth, so we round it up to 1 and add it to 0
please mark brainliest
20, 33, 44, 53, 69, 75, 89, 90 Find the mean and the standard deviation. Round to the nearest thousandth.
The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively
What are mean and standard deviation?The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.
mean= sum of data in the collection/ number of data
= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)
standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data
finding (x- mean)^2 for each value of x
(20-59.125)^2=848.266
(33-59.125)^2=682.516
(44-59.125)^2=228.766
(53-59.125)^2=37.516
(69-59.125)^2=102.516
(75-59.125)^2= 260.016
(89-59.125)^2= 907.516
(90-59.125)^2= 968.766
S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =
√504.484
Therefore S.D =22.461 ( to the nearest thousandth)
learn more about mean and standard deviation from
https://brainly.com/question/26941429
#SPJ1
Question number three in the photo provided.
Using the Central Limit Theorem, the formulas are given as follows:
Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].Mean: [tex]\overline{p} = p[/tex].What does the Central Limit Theorem state?The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
A distribution of proportions, with a proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:
Mean: [tex]\overline{p} = p[/tex].Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
#SPJ1
28-6x=2x-84
Prove: x = 14
28-6x = 2x -84
Add 6x to both sides:
28 = 8x -84
Add 84 to both sides
112 = 8x
Divide both sides by 8
X = 112/8
X = 14
The same number of guests are seated at each of 8 large tables. There are 2 guests seated at one small table. Write an equation to represent the total number of guests T and the number of people x at
each large table. If there are 82 guests, how many are seated at each large table?
Answer:
10
Step-by-step explanation:
Since there are 2 people sitting alone, we can put them aside
then we have 8 large tables, each seat x number of guests
we would have total 8x guests there
so 8x+2=82
then solve
8x=80
x=10
which is an equation of the line through the origin and (-5,6)
The equation of a line through the origin and (-5,6) is y = -1.2x
How to determine the equationIt is important to note that the equation of a line is expressed as;
y = mx + c
Where;
y is the point on the y - axism is the slope of the linex is the point on the x - axisc is the intercept on the y axisFrom the information given, we have the points;
(0, 0) and ( -5, 6)
The formula for slope is given as;
slope, m = y₂ - y₁/ x₂ -x₁
slope, m = 6 - 0/ -5 - 0
slope, m = 6/ -5
slope, m = - 1. 2
To determine the intercept, we have;
6 = -1. 2(-5) + c
expand the bracket
c = 6 - 6
c = 0
The equation is given as;
y = -1.2x
Hence, the equation is y = -1.2x
Learn more about equation of a line here:
https://brainly.com/question/13763238
#SPJ1
suppose that the members of a student governance committee will be selected from the 40 members of the student senate. there are 18 sophomores, 12 juniors and 10 seniors who are members of the student senate. in how many ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors? assume that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee. a. 339 b. 1211760 c. 2160 d. 18643560 e. 25920
Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.
Combination formula:
Cn,x is the number of different combinations of x objects from a set of n elements, given by:
Cnₓ= n!÷ x! (n-x!)
In this problem:
2 sophomores from a set of 18.
2 juniors from a set of 12.
3 seniors from a set of 10.
They are independent, so we can just multiply them, thus:
T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760
The committee can be selected in 1,211,760 ways.
To know more about combinations, refer:
brainly.com/question/24650047
#SPJ4
Which equations pass through the points (1, 3) and (7 9)?
Answer:
f(x)=x+2 Passes through
x-y=2 DOES NOT pass through
Step-by-step explanation:
Method- plug in x and see if the y matches the points. (1,3) (7,9)
f(x)=x+2
f(1)=1+2=3
f(7)=7+2=9
Matches!
x-y=2
1-y=2 --> y=-1
Does not match
What is one solution of this system?
Answer:
C (0,3)
Step-by-step explanation:
Plot the two equations and the points. See the attached graph. The blue area reflects the inequality of y+3x<=8: many points satisfy this equation and they are all blue.
The red line is equation y-3=x. There is only one point on this line that is also in the blue area: (0.3). The other three points (A, B, and D) do not satisfy either equation. The metric term for them is losers.
Kathy and Peter both drive older cars that dont always work in the wintertime. Suppose that Kathy's car works 80% of the time and Peter's works 65% of the time. What is the probability they will both be working on any given morning?
what is y= –12x–6 on a graph
The graph of the equation y = –12x – 6 is attached in the solution.
We can find the x and y intercept of the line to find make the graph.
Putting x = 0 in the given equation, we get:-
y = -12(0) - 6 = 0 - 6 = -6
Hence, the x -intercept is (0,-6).
Putting y = 0 in the given equation, we get:-
0 = -12x - 6
6 = -12x
x = 6/(-12)
x = -1/2
Hence, the y -intercept is (-1/2,0).
We can find another point on the line.
Putting x = -1 in the given equation, we get:-
y = -12(-1) - 6
y = 12 - 6 = 6
y = 6
Hence, another point on the line is (-1,6).
Plotting these points we can graph the equation of the line.
To learn more about graph of the equation, here:-
https://brainly.com/question/1971145
#SPJ1
Can someone solve this I don’t understand the graph
The graph given in the problem is the function of cosine that is;
y = -cos x
How to find the function which was used to make a graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it. If the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has the Amplitude (the maximum distance of the graph from the middle line) = a
Period = [tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
Here we can see that the graph is the function of cosine that is;
y = -cos x
Learn more about finding the graphed function here:
https://brainly.com/question/27330212
#SPJ1
