The fifth term of the geometric progression is -0.125 and the sum of the first 20 terms is [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]
What is a geometric Progression?A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio.
All terms of a geometric progression have a common multiple called the common ratio.
if a = -2, which is first term
r = -0.5 which is common ration,
Then fifth term = a[tex]r^{4}[/tex]
substitute a and r into the above equation, you have
fifth term = (-2)([tex](-0.5)^{4}[/tex] = - 0.125
sum of G.P when the common ratio is less than 1, we have
[tex]\frac{a(1 - r^{n} )}{1 - r}[/tex]
where n = number of terms = 20
sum = [tex]\frac{-2(1 - (-0.5)^{20}) }{1--0.5}[/tex] = [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]
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Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.
f(x)=-3(x+2)²+1
Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2
Graph of Quadratic FunctionThe graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
In the given function;
f(x) = -3(x + 2)² + 1
Axis of symmetry is x = -2vertex = (-2, 1)Kindly find the attached graph of the function below
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) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O
The simple interest that Nike will receive after 2 years is $500.
The principal amount =$5000
Rate = 5% = 0.05
Time = 2 years
Now simple interest = PRT = 5000 × 0.05 × 2 = 500
Hence the simple interest earned by Nike is $500
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.
Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.
A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.
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if Julie average arts test score at 85 and what would you predict her average math test score would be
1. Her Average would be 80
2. Yes, there are more dots around points 80.
Question as shown in the image:
Answer:
arc ABC ≈ 18.2 cm
Step-by-step explanation:
the length of the arc ABC is calculated as
arc = circumference of circle × fraction of circle
the angle around the centre O is 360° , then
angle subtended by arc = 360° - 100° = 260°
then
arc = 2πr × [tex]\frac{260}{360}[/tex] ( t is the radius = 4 )
= 2π × 4 × [tex]\frac{26}{36}[/tex]
= 8π × [tex]\frac{13}{18}[/tex]
= [tex]\frac{8\pi (13)}{18}[/tex]
≈ 18.2 cm (to 3 significant figures )
List 1 4/5, -7/4, 41%, and -1.3 from greatest to least.
The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.
What us descending order?
When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.
Main Body:
To solve this question we need to convert all numbers into decimal system.
calculate:
1 can be written as 1.00
4/5 can be written as 0.8
-7/4 = -1.75
41% = 41/100 = 0.41
-1.3 can remain as it is because it itself is in decimal form.
Hence the order from greatest to smallest is as
1 > 0.8 > 0.41 > -1.3 > -1.75
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The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000. How much will the price decrease in dollars? What
will be the price of the next model?
Decrease in price:
Price of next model:
The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
According to the question,
We have the following information:
The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.
We will find the 13.6% of 42,000 to find the decrease in the price of the next model:
(13.6*42000)/100
$5712
Now, the price of next model will be:
42000-5712
$36288
Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
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A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?
Traveling with the current certain boat went 9 mph against the same boat it only went 1 mph what is the speed of the current how fast would the Bogo if there were no current
If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current is 4km/h and no current is 5km/h.
How to determine the speed?Let b represent the speed of the boat
Let c represent the speed of the current
Downstream:
b + c = 9
Upstream:
b - c = 1
Subtraction
2c = 9-1
2c = 8
Divide both side by 2c
c = 8/2
c = 4 km/h (current)
No current
b = 9 - 4
b = 5 km/h
Therefore the speed is 4km/h and no current is 5km/h.
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help please i am stuck on this problem ??
Answer:
Evaluating the function [tex]f(x)=2x^2[/tex] for the first five positive integers of [tex]x[/tex]:
[tex]f(1)=2(1)^2=2(1)=2[/tex]
[tex]f(2)=2(2)^2=2(4)=8[/tex]
[tex]f(3)=2(3)^2=2(9)=18[/tex]
[tex]f(4)=2(4)^2=2(16)=32[/tex]
[tex]f(5)=2(5)^2=2(25)=50[/tex]
HELP PLEASE HELP I NEED HELP PLEASEEEEEEEEEEE
The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.
What is a linear relation?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
The first and the second differences are:
x y first differences second differences
4 18 ----
5 28 10 ------
6 35 7 -3
7 39 4 -3
8 40 1 -3
9 38 -2 -3
The values of second differences are constant, therefore, the relation is linear.
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In tic-tac-toe, a 3 by 3 grid is filled with X's and O's. How many ways is there to fill the grid so that there is at least 4 of each symbol in the grid?
The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:
252.
What is the arrangements formula?The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:
[tex]A_n = n![/tex]
When the elements arranged can be repeated, the number of arrangements is presented as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.
For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:
5 X's and 4 O's.4 X's and 5 O's.Hence the number of ways to fill up the grid is given as follows:
[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]
Thus 252 ways to fill up the grid.
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HEEELPPPPPPPP Rearrange the formula v = 2gh for h. A) h = v 2g B) h = 2v g C) h = v2 g D) h = v2 2g
Rearranging the equation, making h the subject of the formula, h = v² / 2g
How to rearrange formula?we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.
In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.
In our case the the formula needs to be rearrange to make h the subject of the formula.
Therefore,
v = √2gh
square both sides of the equation
v² = (√2gh)²
v² = 2gh
divide both sides by 2g
v² / 2g = 2gh / 2g
h = v² / 2g
Therefore,
h = v² / 2g
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x− ℎ)^2+kand how they can be identified from the equation.
From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
As given in the question,
Given equation is :
y = A(x-h)² +k
Standard basic parabola equation is y = x² where parabola pass through (0, 0) .
In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .
Value of A > 0 then it open in upward direction .
Value of A <0 then it is open in downward direction.
Vertex of the given parabola y = A(x-h)² +k is (h, k).
Line of symmetry is given by vertical line x =h.
Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
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Richard and two have a combined age of 26. Richard is 5 years old than twice Teos age. How old are Richard and Teo?
Answer:
R = 19 yr old; T = 7 yr old
Step-by-step explanation:
From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.
Thus we have:
[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]
When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14. 5 more than 14 is 19 as 14 + 5 = 19.
Zack and his friends went to a movie on Thursday afternoon. It took 25 minutes to drive to the theater. They arrived at the theater 1 hour and 15 minutes before the movie started. Once it started, the movie lasted for 1 hour and 20 minutes and ended at 4:20 P.M. What time did Zack and his friends leave for the movies
Answer:
2:20
Step-by-step explanation:
The movie started at 3:00 PM they got there at 2:45. and it took them 25 mins to get there meaning they left at 2:20.
Here is the histogram of a data distribution. All class widths are 1
Which of the following numbers is closest to the mean of this distribution?
The number that is closest to the mean of the distribution is 4 (option C)/
What is the mean?A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.
Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.
Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)
Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16
Mean = 64 / 16
Mean = 4
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Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.
Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.
How to determine the unknown information?Since the Ms. Morgan found that 30% of her 120 students are athletes, the known and unknown values include the following:
Known value (whole) = 120 students.
Known value (percent) = 30%
Unknown value (part) = ?
Next, we would determine the unknown value as follows:
Number of athletes = 30/100 × 120
Number of athletes = 30 × 1.2
Number of athletes = 36 students.
Unknown value (non-athletes) = 120 students - 36 students
Unknown value (non-athletes) = 84 students.
Since Mr. Gregory found that 27, or 15%, of his student are athletes, the known and unknown values include the following:
Known value (part) = 27 students.
Known value (percent) = 15%
Unknown value (whole) = ?
For the unknown value, we have:
Let the variable T represent the total number of students.
15/100 × T = 27
0.15T = 27
Total number of students, T = 27/0.15
Total number of students, T = 180 students.
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Complete Question:
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.
b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.
The Roxbury CC Tigers basketball team scored 12 points in the first 6 minutes of a game. If they continue at the same pace, how much will they score during the entire 40 minute game?
84 i think?
im not sure if i did my math properly
Answer:
80
Step-by-step explanation:
40 ÷ 6 = 6.66666667 x 12 = 80
Harry is paid semimonthly. His
Semimonthly salary is $2,052. What is his
annual salary?
Answer:
$12,312
Step-by-step explanation:
$2,052 * 6 = $12,312
A gallon of water contains 128 fluid ounces. A rain barrel can hold 6,400 ounces of rainwater.
Estimate how many gallons of water can the barrel hold?
Answer:
50 gallons
Step-by-step explanation:
6400 ÷ 128
= 50
ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206
Last year when the 6th graders attended camp the ratio of boys to girls was 4:6. If there were 50 more girls how many boys attended camp?
By using concept of ratio, it can be calculated that
100 boys attended the camp
What is ratio?
Ratio between two numbers determines how much one number is greater than the other.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent.
Here, concept of ratio will be used
Let the number of boys be 4x and the number of girls be 6x
There were 50 more girls than boys
By the problem,
6x - 4x = 50
2x = 50
[tex]x = \frac{50}{2}[/tex]
x = 25
Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100
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PLEASE HELP!!!! "CLEVERLY CONICS Portfolio"
Choose one of your conic examples to study in greater detail. Complete the table to create the graph and equation for your chosen example.
1. If possible, use a photo of the structure or item. Otherwise, draw a detailed sketch.
2. Measure and label the key dimensions of the shape in order to duplicate them in a to-scale graph. Be sure to label your units of measure to reflect the actual measurements.
3. Draw the underlying conic section on a coordinate grid.
4. Identify the coordinates of the appropriate key parts of the conic section.
5. Determine the closest approximation of the equation in standard form for the conic section.
Answer:
Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.
BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING
Step-by-step explanation:
When five times a number is decreased by 9 , the result is 26 . What is the number?
Answer:
5x-9=26
Step-by-step explanation:
5x=35
5 5
x = 7
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Answer:
x = 7
Step-by-step explanation:
When five times a number is decreased by 9 , the result is 26 . What is the number?
5x - 9 = 26
add 9 to both sides:
5x - 9 + 9 = 26 + 9
5x =35
divide both sides by 5:
5x/5 =35/5
x = 7
What is the product of the complex numbers below? 7-i / 3+i
Answer: 2-i
Step-by-step explanation:
multiply the fraction by 3-i/3-i
If Ø (theta) is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec Ø (theta) in simplest radical form.
For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.
As given in the question,
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( -9, 5 )
( -9 , 5 ) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = -9
Altitude = 5
Using Pythagoras theorem,
Hypotenuse² = (-9)² + (5)²
⇒ Hypotenuse = √106
cos ∅ = -9 / √106
sec ∅ = 1/ cos ∅
= - √106/9 ( simplest radical form )
Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of
sec∅= ( - √106/ 9 ) in simplest radical form.
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What is the measure of each angle of a regular 22-gon? If necessary, round to the nearest tenth.
The measure of each angle of a regular 22-gon is 163.6 degrees.
How to find the sum of angles of a polygon?In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.
Therefore, a regular polygon is one which sides and angles are congruent.
A regular 22-gon has 22 sides.
The measure of each angle of 22-gon can be found as follows;
angle= 180(n - 2) / n
where
n = number of sides
angle = 180 (22 - 2) / 22
each angle = 180(20) / 22
each angle = 3600 / 22
Therefore,
each angle = 163.636363636
each angle = 163.6 degrees.
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Given the position function:
s(t) = sin t
where t is measured in seconds and
s is measured in feet, find the
average velocity on the interval [0, π].
Please help, i dont understand
The equation of lines are (a) x - 2y + 6 = 0
(b) 2x - y - 4 = 0
(c) x - y + 1 = 0
(d) 4x + 3y + 4 = 0
Slope-intercept form of the equation -> y = mx + c
Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]
(a) A(0,3) and B(6,6)
m = [tex]\frac{6-3}{6-0}[/tex]
= 3/6
= 1/2
Putting the value in equation,
3 = (1/2)*0 + c
c = 3
Equation -> y = (1/2)x + 3
2y = x + 6
x - 2y + 6 = 0
(b) A(0,-4) and B(5,6)
m = [tex]\frac{6+4}{5-0}[/tex]
= 10/5
= 2
Putting the value in equation,
-4 = (2)*0 + c
c = -4
Equation -> y = (2)x - 4
2x - y - 4 = 0
(c) A(-4,-3) and B(2,3)
m = [tex]\frac{3+3}{2+4}[/tex]
= 6/6
= 1
Putting the value in equation,
3 = (1)*2 + c
3 = 2 + c
c = 3 - 2
c = 1
Equation -> y = (1)x + 1
y = x + 1
x - y + 1 = 0
(d) A(-6,4) and B(3,-8)
m = [tex]\frac{-8-4}{3+6}[/tex]
= -12/9
= -4/3
Putting the value in equation,
-8 = (-4/3)*3 + c
-8 = -4 + c
c = -8 + 4
c = -4
Equation -> y = (-4/3)x - 4
3y = -4x - 4
4x + 3y + 4 = 0
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Suppose a basketball player has made 215 out of 322 free throws. If the player makes the next 2 free throws, I will pay you $32. Otherwise you pay me $24. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
The expected value of the proposition is -$1007.41
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Suppose a basketball player has made 215 out of 322 free throws.
This means that p = 215/322 = 0.6677
2 free throws:
This means that
Probability of making two free throws.
This is P(X = 2).
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629
Expected value:
If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.
Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.
E = 0.29629*24 - 31.70371*32 = -1007.41
Hence, The expected value of the proposition is -$1007.41
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