Given the terms
-2, 4, -8, 16
The first term = -2
The second term is 4
The third term is -8
The fourth term is 16
We can observe that this is a geometric sequence
So to get the 11th term, we will first get the formula
Step 1: Get the common ratio (r)
[tex]\text{common ratio=}\frac{\sec ond\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{\sec ond\text{ term}}[/tex][tex]r=\frac{4}{-2}=\frac{-8}{4}=-2[/tex]Step 2: Get the formula for the nth term
The formula is given by
[tex]T=r^n[/tex][tex]T=(-2)^n[/tex]where T is the nth term
n is the number of terms
Step 3: Find the 11th term
[tex]T_{11}=(-2)^{11}[/tex][tex]T_{11}=-2048[/tex]The 11th term is -2048
100 POINTS PLEASE HELP
Lisa is saving for college. The account is modeled by the function: F (x) = 250(1.25)^x , when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
x 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Show your work. (this does not have to be done by hand, but just show what you would enter into the calculator)
Answer:
A. $762.94
B. $896.81
C. $133.87
Step-by-step explanation:
Given function modelling Lisa's saving account:
[tex]\boxed{f(x)=250(1.25)^x}[/tex]
where x is the number of years.
Given table modelling Xavier's savings account:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & 0 & 1 & 2 & 3\\\cline{1-5} g(x) & 200 & 270 & 364.5 & 492.08\\\cline{1-5}\end{array}[/tex]
Part ATo find the amount in Lisa's savings account after 5 years, substitute x=5 into the function:
[tex]\begin{aligned}\implies f(5)&=250(1.25)^5\\&=250(3.051757...)\\&=762.939453...\end{aligned}[/tex]
Therefore, the amount in Lisa's savings account after 5 years is $762.94 (nearest cent).
Part BFirst, create an exponential function to model Xavier's savings account.
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.From inspection of the given table, the initial value (a) is 200.
[tex]\implies g(x)=200b^x[/tex]
To find the value of b, substitute point (1, 270) into the function:
[tex]\begin{aligned}\implies g(1)=200b&=270\\b&=\dfrac{270}{200}\\b&=1.35\end{aligned}[/tex]
Therefore. the function that models Xavier's savings account is:
[tex]\boxed{g(x)=200(1.35)^x}[/tex]
To find the amount in Xavier's savings account after 5 years, substitute x=5 into the found function:
[tex]\begin{aligned}\implies g(5)&=200(1.35)^5\\&=200(4.4840334...)\\&=896.806687...\end{aligned}[/tex]
Therefore, the amount in Xavier's savings account after 5 years is $896.81 (nearest cent).
Part CTo find the positive difference in their accounts after 5 years, subtract Lisa's balance from Xavier's balance:
[tex]\implies 896.81-762.94 =133.87[/tex]
In ΔCDE, m∠C = 86° and m∠D = 58°. Which statement about the sides of ΔCDE must be true?
ANSWER
DE > EC > CD
EXPLANATION
Let us make a sketch of triangle CDE:
Let us first find the measure of angle E.
The sum of angles in a triangle is 180 degrees. This means that:
58 + 86 + 144 + =>
The sine of the angle of a triangle and side opposite that triangle is proportional for every angle and side of a triangle.
That is, the ratio of the sine of an angle and the side opposite that angle is constant for a triangle. This is known as the Sine Law.
This law implies that the bigger an angle of a triangle is, the larger the side opposite it and vice versa.
Therefore, since DE > EC > CD
That is the answer.
Would just like to make sure that my answer is correct.
Answer:
[tex]\text{ -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24})[/tex]Explanation:
Here, we want to simplify the given expression
The basic rule we will be using here is:
[tex]\sin (A\text{ + B})\text{ = SinACosB + CosASinB}[/tex]Thus, we have it that:
[tex]\begin{gathered} \text{ sin(}\frac{\pi}{6}+\frac{\pi}{4})\text{ + sin(}\frac{\pi}{8}+\frac{3\pi}{8}) \\ \\ \sin (\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2}) \end{gathered}[/tex]We use the sine addition formula as follows:
[tex]\sin \text{ A + sin B = 2sin(}\frac{A+B}{2})\cos (\frac{A-B}{2})[/tex]Now, we substitute the last expression into the given addition formula above:
[tex]\begin{gathered} \text{ sin(}\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2})\text{ =2sin(}\frac{\frac{5\pi}{12}+\frac{\pi}{2}}{2})\cos (\frac{\frac{5\pi}{12}-\frac{\pi}{2}}{2}) \\ \\ =\text{ 2sin(}\frac{11\pi}{24})\cos (\frac{-\pi}{24})\text{ = -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24}) \end{gathered}[/tex]1. Which of the following expressions are monomials with degree 2?i) 2x² + 2xii) 2x²iii) x²iv) 2xa. ii and iiib. ii and ivC.iii and iv
Answer
a. ii and iii
Step-by-step explanation
A monomial is a polynomial with only one term.
A binomial is a polynomial with two terms.
The degree of a polynomial is determined by the highest exponent of the x-variable.
i) 2x² + 2x
type: binomial
degree: 2
ii) 2x²
type: monomial
degree: 2
iii) x²
type: monomial
degree: 2
iv) 2x
type: monomial
degree: 1
Then, choices ii and iii are monomials with degree 2
Find the surface area. Leave your answers in terms of T.9 mi
Given:
The shape is
Find-:
The surface area of the cylinder
Explanation-:
The surface area of the cylinder
[tex]A=2\pi rh+2\pi r^2[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ h=\text{ Height} \end{gathered}[/tex]The radius and height of the cylinder
[tex]\begin{gathered} r=\frac{\text{ Diameter}}{2} \\ \\ r=\frac{12}{2} \\ \\ r=6\text{ mi} \\ \\ h=9\text{ mi} \end{gathered}[/tex]The surface area of the shape is:
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ \\ A=2\pi(6)(9)+2\pi(6)^2 \\ \\ A=108\pi+72\pi \\ \\ A=180\pi\text{ mi}^2 \end{gathered}[/tex]The surface area is 180π mi²
indicate the maximum or minimum of value of f(x) whichever exists.
The given function is
[tex]f(x)=x^2-2x-5[/tex]All quadratic functions represent a parabola. If the quadratic term is positive, the parabola opens up, if the quadratic term is negative, the parabola opens down.
In this case, we observe a positive quadratic term, so the parabola opens up, which means the function has a minimum.
To find the minimum of the function, we need to find its vertex (h,k), where
[tex]h=-\frac{b}{2a}[/tex]a = 1 and b = -2.
[tex]h=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Then, evaluate the function to find k.
[tex]f(1)=(1)^2-2(1)-5=1-2-5=1-7=-6[/tex]The k-coordinate of the vertex refers to the minimum value.
Therefore, the answer is -6.
Find the value if n in improper fraction.
The value of n will be equal to -7/2 or [tex]-4\frac{1}{2}[/tex].
This question can be solved using the Laws of exponents. We have the expression 1/8 ÷ √2 = 2ⁿ. We can rearrange this expression as follows
1/(8×√2) = 2ⁿ
We can also write this as
1/(2³·2^1/2) = 2ⁿ
From laws of exponents if bases are same then the powers get add up that is
1/(2^7/2) = 2ⁿ
2^-7/2 = 2ⁿ
From laws of exponents, we compare that the bases are same so the powers will also be same. So, we find that n = -7/2 which can be written in improper fraction as [tex]-4\frac{1}{2}[/tex].
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This year Apple has launched iPhone 14. There are 4 different colors (Silver, gold, space
black, purple) of iPhone 14 Pro Max and iPhone 14 Pro. Also, there are 5 different colors
(Midnight, blue, starlight, purple, red) available for iPhone 14 plus and iPhone 14. How many different types of phones are available this year?
There are 18 different types of phones are available this year.
What is Addition?The process or skill of calculating the total of two or more numbers or amounts.
There are 4 different colors (Silver, gold, space black, purple) for,
iPhone 14 Pro Max → 4
iPhone 14 Pro → 4
There are 5 different colors (Midnight, blue, starlight, purple, red) for,
iPhone 14 plus → 5
iPhone 14 → 5
Add all of them = 4 + 4 + 5 + 5
we get, = 18
Hence, There are 18 different types of phones are available this year.
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The mean of 6 numbers is 7.
The numbers are in the ratio 1 : 1 : 3 : 4 : 5 : 7.
Find the range
The range of the given data set is 6.
What is the range?The gap between the largest and smallest numbers is known as the range. The average of the largest and smallest number is the midpoint. The range is the range of values, from lowest to highest. Example: The lowest value in 4, 6, 9, 3, and 7 is 3, and the highest value is 9. The range is therefore 9 3 = 6.So, the range is:
As we can observe that the ratios are already given in ascending order, then we don't need to solve the question.Instead, just subtract the lowest ratio from the highest ratio as follows:
7 - 1 = 6
Therefore, the range of the given data set is 6.
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The following table shows the cost of apples. Number of 3 5 8 11 Apples (2) $2.37 Cost (y) $3.95 $6.32 $8.69 Assume the cost of apples is a linear function of the number of apples purchased. 39 www Wwwwwwwwwwwwwwww B Part A www Write a linear equation that describes the cost of apples, y, in dollars, as a linear function of the number of apples purchased, I.
We will calculate the linear equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
3=x1
5=x2
2.37=y1
3.95=y2
[tex]m=\frac{3.95-2.37}{5-3}=\frac{1.58}{2}=0.79[/tex]then we will substitute in the next formula
[tex]y-y_1=m(x-x_1)[/tex][tex]\begin{gathered} y-2.37=0.79(x-3) \\ y-2.37=0.79x-2.37 \\ y=0.79x \end{gathered}[/tex]the linear equation is
y=0.79x
in susan graduating class the ration of girls to boys is 3:2 and the total number of students is 250. what is the total number of girls and boys iin susan's graduating class?
Explanation:
The ratio of girls to boys = 3:2
Total number of students = 250
Sum of ratio = 3 + 2 = 5
The total number of girls = 3/5 * 250
7. An internet service provider charges $20 per month plus an initial set-up fee. One customer paid a total of $92 after 2 months of service. Write an equation in point-slope-form modeling this situation. Then, write the equation in slope-intercept form. What does the 52 represent in your slope-intercept form equation?
The internet service provider charges $20 per month plus an initial set-up fee.
Let "x" represent the number of months that are charged, then the monthly fee can be expressed as 20x
Let "y" represent the cost of the internet service after x months.
If the customer paid y=$92 after x=2 months of service, this information represents a point of the relationship that can be expressed as (2,92)
The point-slope form has the following formula:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope
(x₁,y₁) are the coordinates of one point of the line.
The slope of the line corresponds to the monthly fee for the internet service, so m=$20
The coordinates of the point you have to use is (2,92)
So the equation in point-slope form is
[tex]y-92=20(x-2)[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y-92=20\cdot x-20\cdot2 \\ y-92=20x-40 \end{gathered}[/tex]Then pass "-92" to the right side of the equation by adding it to both sides of the equal sign:
[tex]\begin{gathered} y-92+92=20x-40+92 \\ y=20x+52 \end{gathered}[/tex]The equation in point-slope form is y-92=20(x-2)
The equation in slope-intercept form is y=20x+52
$20 is the slope of the equation and represents the monthly fee for internet service.
$52 is the y-intercept of the equation, it represents the initial set-up fee for the internet service.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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Select the equation of a circle with a center at the origin and a radius 7.
The Solution.
The circle with a center at the origin implies that (a,b) = (0,0).
The equation of a circle is given by;
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Where a=0, b=0 and r=7 units.} \end{gathered}[/tex]Substituting the values above into the formula, we get
[tex]\begin{gathered} (x-0)^2+(y-0)^2=7^2 \\ x^2+y^2=49 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
Thus, the correct answer is option C / third option.
[tex]x^2+y^2=49[/tex]Type the correct answer in the box.
Find the value of x in the figure.
Answer:
x = 35
Step-by-step explanation:
An hexagon has 6 sides, so (n-2) is 4, and the internal angles add up to 180° × 4 = 720°
so
4x - 5 + 117 + 3x - 3 + 3x + 6 + 118 + 4x - 3 = 720
14x + 230 = 720
14x = 720 - 230
14x = 490
x = 490 : 14
x = 35
Answer:
x=35
Step-by-step explanation:
8 This graph shows how fast Heidi ran on a track. Heidi says she was
running 1.5 laps per minute because 3/2= 1.5. What mistake did
she make? How fast was Heidi running?
You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
Let
x -----> minutes does Newton walk dogs
y ----> minutes does Descartes walk dogs
z ----> minutes does you walk dogs
so
z=2x ------> equation A
y=3x ------> equation B
x+y+z=3,030 ------> equation C
substitute equation A and equation B in equation C
x+(3x)+(2x)=3,030
solve for x
6x=3,030
x=505 minutes
therefore
the answer is
Newton walk dogs 505 minutesLuther opened a savings account and deposited $400.00. The account earns 4% interest,compounded annually. If he wants to use the money to buy a new bicycle in 2 years, howmuch will he be able to spend on the bike?nt= P(1+7)1Use the formula A = P (1 + r/n)where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.
To solve this problem, we must use the formula:
[tex]A=P\cdot(1+\frac{r}{n})^{t\cdot n}\text{.}[/tex]Where:
• A = final amount = ?,
,• P = starting amount = $400.00,
,• r = interest rate in decimals = 4% = 0.04,
,• n = number of times per year that the interest is compounded = 1 (because interest is compounded annually),
,• t = time in years = 2.
Replacing the data of the problem in the equation above, we get:
[tex]A=400.00\cdot(1+0.04)^2=432.64.[/tex]Answer
After 2 years, he will be able to spend $432.64 on the bike.
√-144
Real number or not real number
Answer:
not a real number
Step-by-step explanation:
Non-real numbers are also called imaginary numbers. Imaginary numbers possess an imaginary component, which exists after taking the square root (or any even root) of a negative number
Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{5x+1}{2-5x}The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer(Answer + Answer)
Answer:
[tex]\begin{gathered} \text{ The numerator of f}^{-1}(x)\text{ is 1-2x} \\ \text{ The denominator of f}^{-1}(x)\text{ is -5(x}+1) \end{gathered}[/tex]Step-by-step explanation:
To find the inverse of a function, replace f(x) by ''y'', then replace ''y'' with and x, and every x with a ''y''. Solve for y.
[tex]\begin{gathered} f(x)=\frac{5x+1}{2-5x} \\ Replace\colon\text{ f(x)}\rightarrow y \\ y=\frac{5x+1}{2-5x} \\ Replace\colon\text{ y}\rightarrow x\text{ x}\rightarrow y \\ x=\frac{5y+1}{2-5y} \\ \text{ Solve for y.} \\ x(2-5y)=5y+1 \\ 2x-5yx=5y+1 \\ -5yx=5y+1-2x \\ -5yx-5y=1-2x \\ y(-5x-5)=1-2x \\ y=-\frac{1-2x}{5x+5} \\ y=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex][tex]\begin{gathered} Replacey\colon f^{-1}(x) \\ f^{-1}(x)=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex]half of the sum of six and three then divided by seven.
Answer:
0.64285714285
Step-by-step explanation:
6+3=9
9 divided by 2= 4.5
4.5 / 7= 0.64285714285
I don't think this is what you're looking for?
Large SmallBlue 17 3Red 8 12?Find: P(Small and Blue)Remember to reduce your answer.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answer:
x = -1
y = 3
Step-by-step explanation:
.............
Graph 8x - 4y = 16, then find its x-intercept & y-intercept.
The y-intercept of an equation is where its graph intersects the y-axis - this happens at x = 0; therefore, putting in x =0 should give us the y-intercept.
Putting in x = 0 gives
[tex]8(0)-4y=16[/tex][tex]\rightarrow-4y=16[/tex][tex]\therefore y=-4.[/tex]Hence, the y-intercept is y = -4.
The x-intercept of an equation is where its graph intersects the x-axis - this happens where y = 0; therefore, the x-intercept is found by putting in y =0:
[tex]8x-4(0)=16[/tex][tex]\rightarrow8x=16[/tex][tex]\therefore x=2.[/tex]Hence, the x-intercept is x = 2.
The graph is attached below.
the table displays the scores of students on a recent exam find the mean of the scores to the nearest tenth
In this case, the number of students refers to frequencies.
To find the mean, we have to use the following formula
[tex]\begin{gathered} \bar{x}=\frac{\Sigma(x\cdot f)}{N}=\frac{65\cdot4+70\cdot1+75\cdot7+80\cdot5+85\cdot8+90\cdot3+95\cdot4+100\cdot1}{33} \\ \bar{x}=\frac{260+70+525+400+680+270+380+100}{33} \\ \bar{x}=\frac{2685}{33} \\ \bar{x}\approx81.4 \end{gathered}[/tex]Hence, the mean is 81.4.. Ross has a spinner that is split into eight equal sections numbered 1 through 8. He spun the spinner 1120 times. Which of the following would be a good estimate of the number of times the spinner landed on number 6?
The probability of the spinner landing on number 6 is calculated as follows:
[tex]\begin{gathered} p=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ p=\frac{1}{8} \end{gathered}[/tex]Given that he spun the spinner 1120 times
The equation P=4s represents the perimeter P of a square with side length s. What is the perimeter of a square with side length 6 mi?
The perimeter is mi.
Answer:
24mi
Step-by-step explanation:
p=4s=4(6mi)
=24mi
4) Find the area of each composite figure. 2.5 in 2.5 in 6 in in? 4.2 in А = square A trapezoid ina А figure 1/1
The figure is a combination of a square and a trapezoid;
Thus, we first look for the area of a square using the formula below;
[tex]\begin{gathered} A_{square}=length\times length \\ \text{Where the length of the square is 2.5in} \\ A_{square}=2.5\times2.5 \\ A_{square}=6.25in^2 \end{gathered}[/tex]Answer: The area of the square is 6.25 square inches.
Also, we find the area of the trapezoid using the formula below;
[tex]\begin{gathered} A_{trapezoid}=\frac{1}{2}(a+b)h \\ \text{Where a and b are the upper length and the bottom length respectively } \\ a\text{ is the length of the square = 2.5in} \\ b=\text{ 4.2in} \\ \text{h is the height = 6in} \\ A_{trapezoid}=\frac{1}{2}(2.5+4.2)6 \\ A_{trapezoid}=3(6.7) \\ A_{trapezoid}=20.1in^2 \end{gathered}[/tex]Answer: The area of the trapezoid is 20.1 square inches.
[tex]\begin{gathered} A_{figure}=A_{square}+A_{trapezoid} \\ A_{figure}=6.25in^2+20.1in^2 \\ A_{figure}=26.35in^2 \end{gathered}[/tex]Answer: The area of the figure is 26.35 square inches.
What is the range of the function
Answer:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
Minimum value of y = 0Maximum value of y = 9As there is an open circle where y = 9, this means the value is not included in the range.
Therefore, the range of the function is:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
There are 13 candidates for homecoming king and 14 candidates for homecoming queen. How many possible outcomes are there for homecoming king and queen ?
Answer:
welll
Step-by-step explanation:
Well we know theres only gonna be one king and one queen so the outcome can be that the other people will obviously not get to be king or queen and the other people will get jealous (im not really sure if im right sory)
