Answers
Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
Related Questions
the marketing department of a company has determined that the profit for selling x units of a product is appropriated by function f(x)= 15× -600
Answers
You have the following function for the profit for selling x units of a product:
f(x) = 15x - 600
in order to determine the profit for 15,600 units, replace x = 15,600 into the previous function and simplify:
f(15,600) = 15(15,600) - 600 = 233,400
Hence, the profit for 15,600 units is $233,400
Write using set-builder notation: -2x + 1 < 27
Answers
Instead of describing the constituents of a set, a set-builder notation describes them. The set-builder notation exists A = {x: x is a natural number less than 27}.
What is meant by set-builder notation?A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Set-builder notation is a mathematical notation for defining a set by enumerating its elements or by specifying the properties that each of its members must satisfy. It is used in set theory and its applications to logic, mathematics, and computer science.
Let the given inequality be 2x+1 < 27
Subtract 1 from both sides, we get
-2x+1-1 < 27-1
Simplifying the above equation, we get
-2 x < 26
Multiply both sides by - 1 (reverse the inequality)
(-2 x)(-1) > 26(-1)
Simplifying the above equation, we get
2x > -26
Divide both sides by 2
[tex]$\frac{2 x}{2} > \frac{-26}{2}[/tex]
x > -13
Therefore, the set-builder notation exists
A = {x: x is a natural number less than 27}.
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Algebraically manipulating the formula FV = P(1 + p", how much money is needed as an initial deposit to reach a future value of $8,700, if the account isearning 7%, compounded quarterly, for 6 years to the nearest whole dollar)?$6,154.33$5,737.11$5,432.19$4,908,66None of these choices are correct.
Answers
The future value formula, given by
[tex]FV=P(1+\frac{r}{n})^{nt}[/tex]Can be used to obtain the Principal by substituting other values into the equation and solving for P
Step 1: List out the parameters given
FV =$8,700
r=7%=0.07
n=4 (since there are 4 quarters in a year)
t=6 (since it will be compounded 6 times a year)
Step 2: Substitute the values into the formula
[tex]8700=P(1+\frac{0.07}{4})^{4\text{ x 6}}[/tex][tex]8700=P(1+0.0175)^{24}[/tex][tex]\begin{gathered} 8700=P(1.0175)^{24} \\ 8700=1.5164P \end{gathered}[/tex]Solving for P
[tex]\begin{gathered} 1.5164P=8700 \\ P=\frac{8700}{1.5164} \end{gathered}[/tex]P=$5737.11
Option B is correct
Make a tree diagramPlease be quick, I am in a hurry.
Answers
Explanation
The question wants us to obtain all the outcomes possible when a coin and a cube is tossed
A coin has two possible outcomes
[tex]\mleft\lbrace\text{Head, Tail}\mright\rbrace[/tex]A cube has 6 surfaces, so the outcomes are
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Thus, we can have the diagram showing the outcomes to be
Which sequence of transformations will change figure PQRS to figure P'Q'R'S'?
Answers
Explanation:
A counterclockwise rotation about the origin by 90 degrees rule is:
[tex](x,y)\rightarrow(-y,x)[/tex]The reflection about the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]If we take for example point P (-3, -2) we can see it ends at P'(2,3). The counterclockwise rotation about the origin by 90º gives:
[tex](-3,-2)\rightarrow(2,-3)[/tex]And now with a reflection about the x-axis:
[tex](2,-3)\rightarrow(2,3)[/tex]Which is point P'
Answer:
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis
which of the following is the equation that represents the function given in the table
Answers
To determine which of the given equations represents the function given in the table, let us analyze each of them.
The first two equations do bring not integer numbers in such a way that, if we substitute any of the x values given, we will find a y value which is not an integer. This means that both are not the ones we are looking for.
Now, to determine if the third or the fourth is the one, let us substitute one of the x values on it, and if the y value matches, it means that it might be correct.
Checking the fourth, let's use the values:
[tex]\begin{gathered} x=-2 \\ y=16 \end{gathered}[/tex]Substituting the value of x in the equation of the fourth option, we have:
[tex]\begin{gathered} y=6\times(-2)-5 \\ y=-12-5 \\ y=-17 \end{gathered}[/tex]Because the y value found was not the one given, the option is wrong!
Let's check the third option with the same values of x and y:
[tex]\begin{gathered} y=-5\times(-2)+6 \\ y=10+6 \\ y=16 \end{gathered}[/tex]It matches. This substitution alone does not assure this is the right answer, but once it can not be anyone of the other three, and once we expect that one of the four is the function, this match becomes enough for our final answer:
C) y = -5x + 6
Barbara puts $500.00 into an account to use for school expenses. the account earns 14% interest, compounded annually. how much will be in the account after 7 years?use the formula A= P ( 1 + ).where A is the balance (final amount), p is the principal ( starting amount), r is the Internet rate express as a decimal, n is number of time per year that the interest is compounded, and T is the time in years. Round, your answer to the nearest cent
Answers
the formula is:
A = P( 1 + r/n )^nt
then solve:
[tex]undefined[/tex]Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
Answers
Solution
Note: Laws Of Logarithm To Use
[tex]\begin{gathered} (1).\text{ }log_a(M)-log_a(N)=log_a(\frac{M}{N}) \\ \\ (2).\text{ }log_a(b^n)=nlog_a(b) \end{gathered}[/tex]From the question, we have
[tex]\begin{gathered} log_3(18)-log_3(2) \\ \\ log_3(\frac{18}{2}) \\ \\ log_3(9)\text{ } \\ \\ The\text{ above expression is single logarithm} \end{gathered}[/tex]To evaluate, we have
[tex]\begin{gathered} log_3(9)=log_3(3^2) \\ \\ log_3(9)=2log_3(3) \\ \\ log_3(9)=2(1) \\ \\ log_3(9)=2 \end{gathered}[/tex]The answer is
[tex]2[/tex]there are 66 utensils in the cafeteria. 22 of them are spoons and the rest are Forks. what is the ratio of the number of spoons to the total number of utensils?And what is the ratio of the number of forks to the number of spoons?
Answers
Let's begin by listing out the information given to us:
Total utensils = 66
Spoons = 22
Forks = 66 - 22 = 44
The ratio of spoons to the total utensil is given by the ratio of spoons to total utensils. We have:
22:66 ⇒ 1:3
Therefore, the ratio of spoons to total utensils is 1 spoon is to 3 utensils
The ratio of the number of forks to spoon is given by the ratio of forks to spoon. We have:
44:22 ⇒ 2:1
Therefore, the ratio of forks to spoon is 2 to 1. For every 2 forks, there is 1 spoon
Can someone help me out??
Answers
The correct option for the missing sides of given triangles is-
Part 1: x = 30Part 2: x = 21Part 3: x = 49Part 4: x = 22What is termed as the similar triangles?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size.For the given question,
The dimension of the two triangles are given with the missing sides.
Part 1: In the given rectangles;
5/3 = x/18
x = 30
Part 2: In the given rectangles;
9/x = 3/7
x = 21
Part 3: In the given triangles;
x/63 = 7/9
x = 49
Part 4: In the given triangles;
16/x = 8/11
x = 22
Thus, the missing sides of the given shapes are found.
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Please help I'm not sure what should I substitute the variable (x) by
Answers
From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
Classify the following triangle. Check all that apply.A. ScaleneB. IsoscelesC. AcuteO D. RightE. EquilateralF. Obtuse
Answers
Answer
Options A and C are correct.
The triangle is a Scalen triangle and it is also an Acute triangle.
Explanation
To answer this question, we first explain what these type of triangles are
According to side lengths,
- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.
- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.
- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.
According to the angles,
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
For this triangle,
We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.
Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.
Hope this Helps!!!
Alejandra categorized her spending for this month into four categories: Rent, Food, Fun, and Other.The percents she spent in each category are pictured here.Food21%Rent30%Other31%Fun18%If Alejandra spent a total of $2500 this month, how much did she spend on Food?
Answers
she spent 525 on Food
she spent 750 on rent
she spent 775 on others
she spent 450 on fun
Explanation
to find the value of the percentage of any number just use this formula
[tex]\text{ percentage=}\frac{\text{ x\%}\cdot\text{ Number}}{100}[/tex]so
to find the values, apply the formula
Step 1
a) food :21 %
so
[tex]\begin{gathered} \cos t\text{ of food=}\frac{\text{ 21}\cdot2500}{100} \\ \cos t\text{ of food=}525 \end{gathered}[/tex]it means she spent 525 on Food
Step 2
b) Rent:30 %
so
[tex]\begin{gathered} \cos t\text{ of rent=}\frac{\text{ 30}\cdot2500}{100} \\ \cos t\text{ of rent=}750 \end{gathered}[/tex]it means she spent 750 on rent
Step 3
c)other:31 %
so
[tex]\begin{gathered} \cos t\text{ of other=}\frac{\text{ 31}\cdot2500}{100} \\ \cos t\text{ of other=}775 \end{gathered}[/tex]it means she spent 775 on others
Step 4
d)Fun:18 %
so
[tex]\begin{gathered} \cos t\text{ of fun=}\frac{\text{ 18}\cdot2500}{100} \\ \cos t\text{ of fun=}450 \end{gathered}[/tex]it means she spent 450 on fun
I hope this helps you
Identify the minimum from the tableType your answer as an ordered pair (x,y)
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By definition, a function is a relation in which each input value has one and only one output value.
The input values are also known as x-values and the output values are also called y-values.
By definition, the Minimum is the lower point of the function.
Having the table shown in the exercise, you can identify the following points:
[tex]\begin{gathered} (-2,10) \\ (-1,8) \\ (0,6) \\ (1,4) \end{gathered}[/tex]You can identify that the lower y-value of all those points is:
[tex]y=4[/tex]Therefore, you can determine that the lower point of the function is:
[tex](1,4)[/tex]The answer is:
[tex](1,4)[/tex]1. Evaluate the following expressions if a = 2. b = 3, x = 4, and y = 5.+3(27-»
Answers
When a=2, b=3, x=4, and y=5,
evaluate:
[tex]b^2+3(2x-y)[/tex]Let's replace b, x and y by the appropriate values:
[tex](3)^2+3(2(4)-5)[/tex]now let's solve what is inside the parenthesis:
[tex]9+3(8-5)[/tex]again more solving inside the second parenthesis:
[tex]9+3(3)[/tex]and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:
[tex]9+9=18[/tex]You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.
Like:
[tex]ab+ya^3[/tex]and then evaluate:
[tex]\frac{y+ab}{b+x}[/tex]I solved the attached equation as 7000 but it seems to ask for a “solution set” did I answer properly?
Answers
The solution set does have only one element: {7000}
A cubic function has turning points at (-1,2) and (1,-2). Which could be its graph?
Answers
ANSWER
Graph D is the correct option
EXPLANATION
The turning points of a function are the points where its derivative changes sign - therefore the slope of the function changes sign. In other words, the turning points are the local maximums and local minimums of the function.
From these options, the one that has a local maximum/minimum at point (-1, 2) and another at point (1, -2) is option D.
Find m∠1 I need help please
Answers
Answer: 70
Step-by-step explanation: 180-110=70
because of isosceles, so ∠1=70
Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.
Answers
The triangle formed is shown in the diagram below
The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
opposite side = 150
adjacent side = 40
Tan x = 150/40 = 3.75
x = Tan^-1(3.75)
x = 75.069
To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees
21 - 7∆ = 4 - 8∆ 5∆ - 3 + 3∆ = ∆ + 7 + 6∆solve these.
Answers
We are given the following equation:
[tex]21-7\Delta=4-8\Delta[/tex]We need to solve for delta, to do that we will first add 8delta on both sides:
[tex]21-7\Delta+8\Delta=4-8\Delta+8\Delta[/tex]Now we add like terms:
[tex]21+\Delta=4[/tex]Now we subtract 21 on both sides:
[tex]21-21+\Delta=4-21[/tex]Adding like terms:
[tex]\Delta=17[/tex]Therefore delta is 17
Find the solution 5(x-9)+3=5x-42A) x=9B) x=-9C) Infinite SolutionsD) No Solutions
Answers
Answer:
C. Infinite Solutions
Explanation:
Given the equation
[tex]5\mleft(x-9\mright)+3=5x-42[/tex]First, open the bracket
[tex]\begin{gathered} 5x-45+3=5x-42 \\ 5x-42=5x-42 \end{gathered}[/tex]Since the left-hand side equals the right-hand side, the system has Infinite Solutions.
Good morning, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.
Answers
6.
(a)
The slope for the side AB is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ B=(5,-2)=(x2,y2) \\ m_{AB}=\frac{y2-y1}{x2-x1}=\frac{-2-(-4)}{5-(-5)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]The slope for the side BC is:
[tex]\begin{gathered} B=(5,-2)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{BC}=\frac{6-(-2)}{7-5}=\frac{8}{2}=4 \end{gathered}[/tex]The slope for the side DC is:
[tex]\begin{gathered} D=(-3,4)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{DC}=\frac{y2-y1}{x2-x1}=\frac{6-4}{7-(-3)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]And the slope for AD is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ D=(-3,4)=(x2,y2) \\ m_{AD}=\frac{4-(-4)}{-3-(-5)}=\frac{8}{2}=4 \end{gathered}[/tex](b) According to the previous results:
[tex]\begin{gathered} m_{AB}=m_{DC} \\ so \\ m_{AB}\parallel m_{DC} \end{gathered}[/tex][tex]\begin{gathered} m_{BC}=m_{AD} \\ so\colon \\ m_{BC}\parallel m_{AD} \end{gathered}[/tex](c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Answers
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
What is the amplitude of the graph g(x)=f(x)+2 Where f(x)=cos x
Answers
In the cosine equation
[tex]y=AcosB(x-C)+D[/tex]A is the amplitude
B is using it to find the period
C is the phase shift
D is the vertical shift
Since the given function is
[tex]g(x)=cos(x)+2[/tex]A = 1
B = 1
C = 0
D = 2
The amplitude is 1
The answer is 1
I need assistance on understanding chapter 6 for ap stats
Answers
Answer:
A) 0.35
B) Expected value = 37.4 passengers
C) Standard deviation = 1.24 passengers
Explanation:
Part a.
The sum of all the probabilities should be 1, so we can calculate the missing probability as follows:
0.1 + 0.1 + 0.3 + x + 0.1 + 0.05 = 1
Solving for x, we get:
0.65 + x = 1
x = 1 - 0.65
x = 0.35
Then, the missing probability is 0.35
Part b.
The expected value is equal to the sum of each number of passengers multiplied by its respective probability, so:
E = 35(0.1) + 36(0.1) + 37(0.3) + 38(0.35) + 39(0.1) + 40(0.05)
E = 3.5 + 3.6 + 11.1 + 13.3 + 3.9 + 2
E = 37.4
Therefore, the expected value is 37.4 passengers
Part c.
To find the standard deviation, we first need to calculate the square of the difference between each value and the expected value, so
x (x - E)²
35 (35 - 37.4)² = 5.76
36 (36 - 37.4)² = 1.96
37 (37 - 37.4)² = 0.16
38 (38 - 37.4)² = 0.36
39 (39 - 37.4)² = 2.56
40 (40 - 37.4)² = 6.76
Then, the variance will be the sum of these values multiplied by its probability, so
Variance = 5.76(0.1) + 1.96(0.1) + 0.16(0.3) + 0.36(0.35) + 2.56(0.1) + 6.76(0.05)
Variance = 0.576 + 0.196 + 0.048 + 0.126 + 0.256 + 0.338
Variance = 1.54
Finally, the standard deviation is the square root of the variance
Standard deviation = √(Variance)
Standard deviation = √(1.54)
Standard deviation = 1.24
Therefore, the standard deviation is 1.24 passengers. and it is a measure of the dispersion, it says how far are the numbers from the mean.
Then, the answers are:
A) 0.35
B) Expected value = 37.4 passengers
C) Standard deviation = 1.24 passengers
Triangle XYZ is rotated 90° counterclockwise about the origin.The result is Triangle X'Y'Z', as shown below.
Answers
A shortcut for a 90° counterclockwise rotation:
• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).
Answer:
Therefore the coordinates would be:
• X,(-5, 3) → ,X',(-3, -5)
,• Y,(-1, 1) → ,Y',(-1, -1)
,• Z,(-8, -4) → ,Z',(4, -8)
Then, the rule is (x, y) → (-y, x).
It goes from -1 to 1 on the x axis.
Answers
ANSWER :
EXPLANATION :
Will mark as brainlist
Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answers
A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
An exam has 2 papers each scored differently. one is out of 120 and another is out of 80. Maryam scores 65% on the first and 80% on the second. work Maryam's total percentage score for her exam.
Answers
Maryam's total percentage score on her exam is 71%.
What is the total percentage score?
Percentage is the ratio of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
The first step is to determine the score on each paper.
Score on the first test = 65% x 120
(65 / 100) x 120 = 78
Score on the second test = 80% x 80
0.80 x 80 = 64
Total percentage score = (sum of scores / total score) x 100
Sum of scores = 64 + 78 = 142
Total score = 120 + 80 = 200
(142 / 200) x 100 = 71%
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A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post
Answers
A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post
we have that
see the attached figure to better understand the problem
so
tan(55)=h/25
solve for h
h=25(tan(55))
h=35.7 ft