Answer:
[tex]a_n = 8(-5)^{n-1}[/tex]
The fifth term of the sequence is 5000.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio. The nth term of a geometric sequence is:
[tex]a_n = a_1(r)^{n-1}[/tex]
a = 8; r = -5
Thus:
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_n = 8(-5)^{n-1}[/tex]
Fifth term:
This is [tex]a_5[/tex]. So
[tex]a_5 = 8(-5)^{5-1} = 5000[/tex]
The fifth term of the sequence is 5000.
Given that E is the universal set and that A and B are subsets of E. simplify An(B-A)
Answer:
Answer a h bro ok bye bro good luck
Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants.
Class Frequency
8.26 20
10.01-11.75 38
11.76 36
13.51-15.25 25
15.26-17.00 27
Sample Variance: ___________
Sample Standard Deviation: _________
Answer:
(a) The sample variance is 16.51
(a) The sample standard deviation is 4.06
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}[/tex]
Solving (a); The sample variance.
First, calculate the class midpoints.
This is the mean of the intervals.
i.e.
[tex]x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13[/tex]
[tex]x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88[/tex]
[tex]x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63[/tex]
[tex]x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38[/tex]
[tex]x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13[/tex]
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}[/tex]
Next, calculate the mean
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}[/tex]
[tex]\bar x = \frac{1845.73}{146}[/tex]
[tex]\bar x = 12.64[/tex]
Next, the sample variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
So, we have:
[tex]\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}[/tex]
[tex]\sigma^2 = \frac{2393.6875}{145}[/tex]
[tex]\sigma^2 = 16.51[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{16.51}[/tex]
[tex]\sigma = 4.06[/tex]
12 Jy
10
Which statement is true regarding the graphed
functions?
g
18
f(
4
Of(0) = 2 and g(-2) = 0
Of(0) = 4 and g(-2) = 4
Of(2)= 0 and g(-2) = 0
Of(-2) = 0 and g(-2) = 0
2
3 4
5 6 x
t6 -5 -3 -2 -12
-4
16
8
10
-121
Mark this and retum
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Given:
The graphs of the function f(x) and g(x).
To find:
The correct statement for the given graph.
Solution:
From the given graph it is clear that, the function f(x) passes through the points (0,4) and (2,0). So,
[tex]f(0)=4[/tex]
[tex]f(2)=0[/tex]
[tex]f(-2)\neq 0[/tex]
The graph of the function g(x) passes through the point (-2,0). So,
[tex]g(-2)=0[/tex]
Since [tex]f(2)=0[/tex] and [tex]g(-2)=0[/tex], therefore the correct option is C.
The graphs of the given functions, f(x), and g(x), bounces off the x-axis.
Correct response:
The true statement regarding the graphed function is the option;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0 }[/tex]Method used to find the true statementThe properties of the graph of f(x) and g(x) are;
When x = 0, the value of f(x) is; f(0) = 4
Therefore;
f(0) = 4
When x = 2, the value of f(x), which is the point on the graph corresponding to a x-value of 2 is; [tex]\underline{f(2) = 0}[/tex]
When x = 0, g(x) value is g(0) = 4
When x = -2, g(x) is; g(-2) = 0
The correct option is therefore;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0}[/tex]Learn more about functions here:
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question- pls help me find the answer
Answer:
(d) -1
Step-by-step explanation:
Hope you have good grades and study well..btw make me as brainliest....ty sweetie
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 108 disks are summarized as follows: Shock Resistance Scratch Resistance High Low High 55 10 Low 13 30 Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. If a disk is selected at random, determine the following probabilities. P(A)=86/100P(B)=79/100P(A')=7/50P(A U B)=95/100P(A' U B)= ???
Answer:
i) 0.63
ii) 0.37
iii) 0.37
iv) 0.77
v) 0.51
Step-by-step explanation:
Total resistance value = 108
A = high shock resistance
B = high scratch resistance
when a disk is selected at random
i) P(A) = P ( high shock resistance )
= ( 55 + 13 ) / 108
= 68/108 = 17/27 = 0.63
ii) P( B ) = P ( high scratch resistance )
= ( 10 + 30 ) / 108
= 40 / 108 = 10/27 = 0.37
iii) P(A') = 1 - P(A)
= 1 - 17/27 = 10/27 = 0.37
iv) P( A U B ) = P(A) + P(B) - P( A n B )
= 0.63 + 0.37 - 0.233
= 0.766 ≈ 0.77
v) P( A' U B ) = P(A') + P(B) - P(A n B )
= 0.37 + 0.37 - 0.233
= 0.507 ≈ 0.51
Whats the equavalent to log8 64+log8 8
In the figure, ∆ALM ≅ ∆BLM by Side-Angle-Side (SAS). Which angles are congruent by CPCTC?
Answer:
C. L LAM = L LBM
Step-by-step explanation:
__________
need help with algebra question ‼️
Answer:
c
Step-by-step explanation:
There are three types of variations.
1. Direct
2. Inverse
3. Joint
There is positive proportionality is two variables are positively related to each other.
The equation for direct proportionality =
y = bx
where y = dependent variable
b = constant
x = independent variable
if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
the equation that represents inverse proportion :
where b = constant of proportionality
Joint variation occurs when the dependent variables value is determined by two or more values
For example, the volume of a cylinder is dependent on the value of the radius and height
What additional information do you need to prove triangle ABC ~ triangle JKL
Answer:
no additional information will help because the triangles are not similar
Step-by-step explanation:
Similar triangles have 3 pairs of congruent, corresponding angles.
Let's look at triangle ABC. Two angle measures are given: 51 deg and 63 deg.
180 - 51 - 63 - 66
The measure of the thrid angle is 66 deg.
One anlgle measure of triangle JKL is given. It is 66 deg.
Since <J is not congruent to any angle of triangler ABC, the triangles are not similar.
Answer: no additional information will help because the triangles are not similar
Which angle is coterminal with a 130° angle? A. An angle measuring –130° O B. An angle measuring 310° C. An angle measuring 490° O D. An angle measuring 480°
Answer:
Option C
Step-by-step explanation:
Positive coterminal angle of 130° is
(130+360)°
= 490°
Answered by GAUTHMATH
Answer:
An angle measuring 490
Step-by-step explanation:
it was right
What is the probability that they both choose a card labeled dog?
Answer:
0.16
Step-by-step explanation:
As it is stated that the card having the label of a dog has a probability of 0.4. Hence, the probability that they both choose a card labeled dog is 0.16.
which of the following does not describe a rigid motion transformation
Answer:
The answer to this question is dilating the figure by a scale factor of one half.
What is the quotient of the fractions below? 2/3÷5/4
answer:
2/3÷5/4 is equal to 8/15
What's the area
5.1 5.1 5.1 ?
Answer:
Are you talking about the are of a 3d cube? then it would be 156.06 because you take the length times width to get the area of one side then multiply it by 6 to gets all the sides.
20 POINTS- Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
A 4-column table with 5 rows titled Vacation Preferences. Column 1 has entries beach, big city, camping, skiing, total. Column 2 is labeled spring with entries 35, 7, 14, 4, 60. Column 3 is labeled summer with entries 10, 2, 8, 10, 30. Column 4 is labeled total with entries 45, 9, 22, 14, 90.
Complete each statments.
About ____% of the students surveyed prefer a spring camping vacation.
About ____% of the students surveyed prefer a big city vacation.
Answer:
The answers for edge 2021 is
Step-by-step explanation:
16 and 10
Arithmetic or geometric 18,13,8
Answer:
That is Arithmetic
Step-by-step explanation:
Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity. Which is -5 in this case.
Hope this helps
4 pillows and 5 quilts cost £53, 6 pillows and 5 quilts cost £57, find the cost of one each
Answer:
p=2
q=9
Step-by-step explanation:
4p+5q=53
6p+5q =57
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
The sample space,S,of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.
Answer: Bottom left corner
=======================================================
Explanation:
There are only four possible outcomes here
A) we get all tails, ie getting 0 headsB) we get exactly one head (the rest tails)C) we get exactly 2 headsD) we get all three headsBased on this so far, the answer is either the table in the bottom left corner or in the top right corner. It's not possible for X = 4 since we only flipped 3 coins.
The probability of case A happening is 1/8 since we have 1 scenario that's all tails (TTT) out of 8 items in the sample space. Similarly, the probability for case D is the same probability. We only have one HHH out of 8 total items.
The probabilities of cases B and C are the same. Both are 3/8. Note that for case B, we have HTT, THT, TTH which is three occurrences in which we get exactly 1 head. So that explains the 3/8.
If the sum of the interior angle of a polygon is 2700 how many sides does the polygon have??
=================================================
Work Shown:
S = sum of all interior angles of a polygon
S = 180(n-2)
2700 = 180(n-2)
180(n-2) = 2700
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
There are 17 sides to this polygon.
-------------------------
Extra info (optional section):
We call this a 17-gon. Simply start with "n-gon" and replace n with 17.
You could also call it a heptadecagon
hepta = 7
deca = 10
so heptadeca means 17. Personally, I prefer 17-gon as the better name since it's easier to remember.
f h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?
Answer:
here is your answer
Step-by-step explanation:
here is your answer
A book store had 30816 exercise books which were paclced in cartons each carton contained 24 exercise books the mass of an empty carton was 2kg and a full carton 12kg
30,816 books would go into 1,284 containers which would weigh 15,408kg with all the books in them or 2,568kg with the books not in them.
WILL MARK YOU IF YOU ANSWER SO PLEASE HELP
Answer:
x= 83
first take vertical opposite angle then take corresponding angles then you're done
Answer:
x value is 83 degree
because they both are alternate exterior angle
Find the volume and surface area of the rectangular solid. The length is 4 meters, the width is 6 meters, and the height is 3 meters.
Answer:
Volume = h * w * l (height, width, length)
Volume = 4* 6 * 3
Volume = 72 cube meters
Surface area is finding the are of every 2D plane on the solid.
2(w * h) + 2(l*h) + 2(w * l)
Surface are = 108 square meters
what is the slope of this graph?? :,)
Answer:
1/2
Step-by-step explanation:
This line is going up towards the right- that makes it positive. It is increasing. So it can't be negative or going "down"
The question wants to see if you know the direction of the line.
Need help finding the end behavior !
Let's focus on f(x) = |x| for now.
Recall that the absolute value of any number is never negative.
Some examples: |-7| = 7 and |5| = 5
So as x gets bigger in the positive direction, so does y. That explains the notation [tex]x \to \infty, \ f(x) \to \infty[/tex]. Informally, we can say "the graph rises to the right".
Similarly, we have [tex]x \to -\infty, \ f(x) \to \infty[/tex] which means it "rises to the left". Both endpoints rise to positive infinity. The left side of the graph goes up forever because again the result of any absolute value function is never negative. So if we plug in say negative a million, then the result is positive a million. In a sense, the V shape absolute value function is almost like a parabola. Both have the exact same end behavior on both sides.
---------------------------------------------------------------------------------------
Now let's move onto g(x) = 2x^2+4
The only thing that matters when determining the end behavior is the leading term. The leading term here is 2x^2
The even exponent means the endpoints either A) go up together or B) go down together. We go with case A because the leading coefficient is positive. Like I mentioned earlier, this parabola mimics the V shaped absolute value graph in terms of the end behaviors being the same.
---------------------------------------------------------------------------------------
Lastly, let's focus on h(y) = 3y^4-2
I'm not sure why your teacher is using y when the others were using x. I'll just swap y for x to get h(x) = 3x^4-2
Like the g(x) function, the largest exponent is even, so the left and right end behaviors go in the same direction. The positive leading coefficient means we have the endpoints going upward toward positive infinity.
Identify the pairs of congruent angles and proportional corresponding side lengths
Answer:
∠B=∠D, ∠C=∠E, ∠A=F.
Step-by-step explanation
FE/AC=6/8=3/4, FD/AB=9/12=3/4,DE/BC=13.5/18=3/4. Since all proportions are equal to 3/4, the corresponding side lengths are proportional.
The value of the expression
2x²
+ x(100 - 15x) when x = 5 is
Х
0 119.
0 129.
135.
0 145.
Answer:
f(5) = 75
Step-by-step explanation:
The function is f(x) = 2x^2 + x(100 - 15x).
Evaluate this function at x = 5: replace each instance of x with 5:
f(5) = 2(5)^2 + 5(100 - 15·5)
Order of operations rules require evaluating the expression enclosed in parentheses first. We get:
f(5) = 2(5)^2 + 5(100 - 15·5)
= 50 + (100 - 75), so that:
f(5) = 50 + 25 = 75
f(5) = 75
Answer:
175?
Step-by-step explanation:
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?
Answer:
The length of BC is 14 units.Step-by-step explanation:
[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]
The length of B'C' is 0 units.
What is translation?It is the movement of the shape in left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The length of AD = 5 units.
Since the rectangle translates down by 4 units,
The length of A'D' =5 units.
The width of the original rectangle is AB, which is 3 units.
Since the rectangle translates to the right by 2 units,
The width of the new rectangle = 3 units.
Now,
The length of B'C' is the same as the length of AD', which is 5 units.
Subtracting 5 units from 5 units gives us a length of 0 units.
Thus,
The length of B'C' is 0 units.
Learn more about translation here:
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Find the volume. Help please it’s due tomorrow
Answer:
2cm
Step-by-step explanation:
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I need help with this problem
Answer:
x = 21, y = 40
Step-by-step explanation:
The angle above (7x - 13) is (2x + 4 ) ← alternate angle
(7x - 13) and (2x + 4) are adjacent angles and sum to 180° , then
7x - 13 + 2x + 4 = 180
9x - 9 = 180 ( add 9 to both sides )
9x = 189 ( divide both sides by 9 )
x = 21
Then
2x + 4 = 2(21) + 4 = 42 + 4 = 46
(2x + 4) and (3y + 14) are adjacent angles and sum to 180° , so
46 + 3y + 14 = 180
60 + 3y = 180 ( subtract 60 from both sides )
3y = 120 ( divide both sides by 3 )
y = 40