Answer:
The 8th term of the following sequence is 9375.
Step-by-step explanation:
Given the sequence
3/25, 3/5, 3, 15
As we know that a geometric sequence has a constant ratio and is defined by:
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
so
[tex]\frac{3}{25},\:\frac{3}{5},\:3,\:15[/tex]
[tex]\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5[/tex]
As the ratio 'r' is the same.
so
[tex]r=5[/tex]
As the first element of the sequence is
[tex]a_1=\frac{3}{25}[/tex]
Therefore, the nth term is computed by
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=\frac{3}{25}\cdot \:5^{n-1}[/tex]
Putting n = 8 to determine the 8th term.
[tex]a_8=5^7\cdot \frac{3}{25}[/tex]
[tex]a_8=\frac{3\cdot \:5^7}{25}[/tex]
[tex]=\frac{5^7\cdot \:3}{5^2}[/tex]
[tex]=5^5\cdot \:3[/tex]
[tex]=9375[/tex]
Therefore, the 8th term of the following sequence is 9375.
Find the zeros of each function. Part 3. Please show work.
1. f(x)= x^4 - x^3 - x^2 - x - 2
2. f(x)= x^3 - 8x^2 + 19x - 12
9514 1404 393
Answer:
real: -1, 2; complex: +i, -i1, 3, 4Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
__
2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
__
I have attached a spreadsheet that does synthetic division. There are web sites that will do this, too. The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1). When you fill in the zero and coefficients, the built-in formulas do the rest.
9514 1404 393
Answer:
real: -1, 2; complex: +i, -i
1, 3, 4
Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
__
2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
__ The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1).
andy is scuba diving he starts at sea level and then descends 10 feet in 2 1/2 minutes. how would you represent andy’s descent as a unit rate? express your answer as an integer
Answer:
4 feet/minute
explanation:
The rate of descent = (10 feet)/(2.5 mn) = 4 ft/min
3) g(x) = 4x
h(x) = -3x^2 + 4
Find (g + h)(x)
Answer:
The answer is the last line below.
Step-by-step explanation:
g(x) = 4x
h(x) = -3x^2 + 4
(g + h)(x) = 4x - 3x^2 + 4
Tristen's cat had 3 baby kittens. Each kitten weighed 1 pounds. How many ounces did all of his kittens weigh together?
PLEAS HELP ME I WILL GIVE YOU FREE ROBUX PLEASE HELP ME ON THIS ANSWER
Question:Name each polygon by its number of sides and then classify it as CONVEX or CONCAVE and REGULAR or IRREGULAR
Answer:
1.Nonagon-convex, regular
2.Quadrilateral-convex, irregular
3.Hexagon-concave, irregular
Answer:
1.-Nonagon-convex, regular
2.-Quadrilateral-convex, irregular
3.-Hexagon-concave, irregular
what is the area of a rectangular garden that is 60 feet by 20 feet
PLEASE HELP (ASSIGNMENT DUE IN 20 MINUTES)
Answer:
11 widgets
Step-by-step explanation:
544.50/4.5 = 121
square root 121 = 11
Which problem has a sum or difference of 7/12 ? Mark all that apply.
A. 3/4 + 1/6
B. 3/4 - 1/6
C. 1/3 + 1/4
D. 1/4 + 1/6 + 1/12
E. 2/3 - 1/12
F. 2/3 + 1/6
will mark you brainliest
Answer:
a and b
Step-by-step explanation:
Simplify the expression.
13[6^2/(5^2 - 4^2)+9]
Answer:
The simplified term for the given expression is 169.
Step-by-step explanation:
Solving within the parenthesis, given the expression:
13{6^2/(5^2-4^2)+9}
13{36/(25-16)+9}
13{36/9+9}
13(9+4)
13(13)
Therefore, the simplified term in terms of the expression, 13(6^2/5^2-4^2)+9), is 169.
Answer:
169 aidan talk to meee
Step-by-step explanation:
1.1 4 = 22
(4)2 = (22)2 = 24
(62)
13 • (————————— + 9)
(52 - 24)
3.1 6 = 2•3
(6)2 = (2•3)2 = 22 • 3 (22•32)
13 • (——————— + 9)
9 (22•32)
Simplify ———————
9
4.1 Canceling out 32 as it appears on both sides of the fraction line
13 • (4 + 9) gives you 169
Find the value of x and y.
Answer:
x = 30
y = 2
Step-by-step explanation:
Please note: the value for x is correct only if this triangle is a right triangle.
This can be solved because 2(5y) = 20 and because if a triangle has all congruent angles then its side lengths are also congruent.
What is 12 percent of 12
Answer:
1.44
Step-by-step explanation:
because I am smart
Help now fast please
Answer:
3/4 or .75
Step-by-step explanation:
slope = dy/dx
dy = 1 - -2 = 3
dx = 2 - -2 = 4
slope = 3/4
Step-by-step explanation:
(1+2)/(2+2)= 3/4 is the slope
TJ-Maxx offered a 40% discount off the original
price of a head board. The amount of the discount
is $14. What is the regular price of the head
board?
HELP THIS IS IMPORTANT!!!!!!!!!
The numbers 1 to 13 are written on 13 separate slips of paper and placed into a box. A slip of paper is randomly drawn from the box. Express probabilities as reduced fractions and as decimals rounded to 3 decimal places. 1. a. What is the probability that the slip of paper has an odd number on it? 1. b. What is the probability that the slip of paper has a number less than 4 on it? Theoretical probability can be used to predict the likelihood of an event. If a single, 6-sided die is rolled there are six possible outcomes. That is, after rolling the die, the side facing up will show one of six possibilities: 1, 2, 3, 4, 5, or 6. The theoretical probability that the die would land with a "2" on the side facing up is P = 1/6 = 0.167 because one out of the 6 possibilities is a "2." MGF2106 Project 2B; SP2020 5 2. Two experiments are conducted in which a single 6-sided die is rolled 20 and 80 times. The outcomes of the experiments are shown below. For each result calculate the experi
Answer: 1a. 0.538
1b. 0.231
Step-by-step explanation:
For Section A.
Given data:
Numbers to be drawn = 1 to 13
Odd numbers = 7
Even numbers = 6
1a. Probability of drawing an odd number
= 7/13
= 0.538
1b. Probability of drawing a number less than 4.
= 3/13
= 0.231
Section B.
You need to provide me with the table containing the data, for me to be able to assist you with it.
8 The fourth grade had 363 students. Over winter break, 94 students moved away, but
26 new students moved in.
а
How
many students are now in fourth grade Show your work.
There are now
students in fourth grade
Answer:
the answer is 295 students
Answer:
363-94+26 = 295 students
The _________ of a hypothesis test is the probability (1minus beta) of rejecting a false null hypothesis.
Answer:
Power
Step-by-step explanation:
An hypothesis is usually formulated at the beginning of research, it is usually in line with the problem statement and gives the possible outcome.
An hypothesis is either accepted or rejected.
Power in hypothesis is the probability of rejecting null hypothesis when it is false. It helps in making a correct decision by rejecting the null hypothesis when it is not true.
power ranges between 0 to 1 when it is close to 1 it is said to be very strong and has the probability of rejecting a null hypothesis when it is not true.
Power helps to avoid a type II error in statistics.
Please help as soon as possible
Answer:
[tex]x=5[/tex] is the required digit that can be used to correctly complete the equation.
Step-by-step explanation:
Given the equation
_____ × 1/10 = 1/2
Let 'x' be the required digit
If we put x=5 the L.H.S will be equal to R.H.S.
i.e.
5 × 1/10 = 5/10 = 1/2
so the equation becomes
5 × 1/10 = 1/2Therefore, [tex]x=5[/tex] is the required digit that can be used to correctly complete the equation.
7.Which equation is a quadratic model for the data set?
A) y=1.1556x^1.9375
B) y=11.6018*1.2207^x
C) y=20.9330x-93.8918
D) y=1.2246x^2-5.0511x+24.288-
The quadratic model for the data set is y = 1.2246x² - 5.0511x + 24.288
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
Polynomials are classified based on degree as linear, quadratic, cubic etc.
The standard form of polynomial (of degree 2) is:
y = ax² + bx + c
The quadratic model for the data set is y = 1.2246x² - 5.0511x + 24.288
Find out more on polynomial at: brainly.com/question/2833285
How many terms are in the expression, 4x + 5y + 15?
Answer:
There are 3 terms.
Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1 3 (y2 + 2)3/2, 3 ≤ y ≤ 4
Answer:
21π/2
Step-by-step explanation:
94.55π is the area of the required surface.
What is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis?[tex]S=\int\limits^{x_1}_{x_2} {2\pi f(x)\sqrt{1+f'(x)^2} \, dx[/tex]
is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis
How to solve the problem?Given,
[tex]x=\frac{1}{3}(y^2+2)^{\frac{3}{2}}[/tex]
[tex]\implies (3x)^\frac{2}{3}=y^2+2\\\implies y^2=(3x)^\frac{2}{3}-2[/tex]
[tex]\implies y=\sqrt{(3x)^\frac{2}{3}-2}[/tex]
Let
[tex]y=\sqrt{(3x)^\frac{2}{3}-2}=f(x)[/tex]
Now, the range of y is given 3≤y≤4
hence, the range of x is [tex](\frac{1}{3}(3^2+2)^{\frac{3}{2}}[/tex],[tex]\frac{1}{3}(4^2+2)^{\frac{3}{2}})[/tex]=(12.16,25.46).
So, [tex]S=\int\limits^{25.46}_{12.16} {2\pi f(x)\sqrt{1+f'(x)^2} dx\\\\=[\frac{\pi}{2}(3x)^{\frac{4}{3}}-\pi (3x)^{\frac{2}{3}}]^{25.46}_{12.16}\\=101.63\pi - 6.99 \pi \\= 94.55 \pi[/tex]
is the area of the required surface.
Hence, 94.55π is the area of the required surface.
Learn more about the area of surface- brainly.com/question/24126051
#SPJ2
Find the area of a compound shape
The answer is 357 m^2
I just need the steps.....
9514 1404 393
Answer:
figure the areas of the rectangle and semicircleadd them togetherStep-by-step explanation:
The area of the rectangle is given by ...
A = LW
A = (20 m)(14 m) = 280 m²
__
The area of the semicircle is ...
A = (1/2)πr²
A = (1/2)π(7 m)² = 24.5π m² ≈ 77 m²
__
Then the total area is ...
280 m² +77 m² = 357 m²
_____
The width of the rectangle is the diameter of the circle, which is twice its radius. The area of a semicircle is 1/2 the area of a circle.
Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
Answer:
She will not have enough money
Step-by-step explanation:
0.79x85=67.15
67.15+35=105.15
The Wilson family had 6 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had at least 4 girls and at most 4 girls?
How many tiles are there in figure 0?
Answer:
40 is the answer
friend me
Which inequality is true?
----
>
-3
-2.
-1
0
1
2
3
0 1 / 2 < -1 2 3
0-2 / 5-17 /
0 -2/3-1-1
/4
Answer:
-3,-2,-1,0,1,2,3
Step-by-step explanation:
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 4 miles per hour and walk at 4 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time?
Answer:
The answer is "0.45385".
Step-by-step explanation:
The time is taken to reach the coast [tex]= \frac{\sqrt{(2^2 + x^2)}}{4}[/tex]
The time is taken to reach Q after reaching the coast [tex]= \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]
Total time, [tex]T= \frac{\sqrt{(1 + (3-x)^2)}}{4}+ \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]
This has to be minimum,
[tex]\to \frac{dt}{dx} = 0[/tex]
[tex]\to \frac{\sqrt{(2^2 + x^2)}}{2} + \frac{\sqrt{1 + (3-x)^2}}{3}\\\\ \frac{x}{4}\sqrt{(4+x^2)} + \frac{(x-3)}{(4\sqrt{(x^2-6x+10)}} = 0\\\\\frac{x^2}{16} \times (4+x^2) = \frac{(x-3)^2}{16 \times (x^2-6x+10)}\\\\x^2(4+x^2) = \frac{(x-3)^2}{(x^2-6x+10)}\\\\4x^2+x^4 = \frac{ x^2+9-6x}{(x^2-6x+10)}\\\\ 4x^2+x^4(x^2-6x+10) = x^2+9-6x\\\\4x^4-24x^3+40x^2+x^6-6x^5+10x^4= x^2+9-6x\\\\x^6-6x^5+ 14x^4-24x^3+39x^2+6x-9=0\\\\[/tex]
x=0.45385
Find the coordinates of the midpoint of the segment whose endpoints are R(9, 3) and S(-1, -9).
Answer:
[tex](4, -3 )[/tex]
General Formulas and Concepts:
Pre-Algebra I
Order of Operations: BPEMDASAlgebra I
Midpoint Formula: [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]Step-by-step explanation:
Step 1: Define
R (9, 3)
S (-1, -9)
Step 2: Find midpoint
Substitute: [tex](\frac{9-1}{2}, \frac{3-9}{2} )[/tex]Subtract: [tex](\frac{8}{2}, \frac{-6}{2} )[/tex]Divide: [tex](4, -3 )[/tex]can someone please help me with this
Answer:
10.) y=-3x+5
11.) y= -1/2 x+2
Step-by-step explanation:
step by step attchaed below
Find m angle f to the nearest degree
Answer:
∠F ≈ 53°
General Formulas and Concepts:
Trigonometry
sin∅ = opposite over hypotenusesin inverse evaluates "backward" to find the measure angleStep-by-step explanation:
Step 1: Define
Looking at ∠F
opposite leg of ∠F = ED = 8
hypotenuse = FE = 10
Step 2: Find m∠F
Substitute: sin∠F = 8/10Simplify: sin∠F = 4/5Take sin inverse: ∠F = sin⁻¹(4/5)Evaluate: ∠F = 53.1301°Round: ∠F ≈ 53°Find the slope of the line through each pair of points plz
Answer:
-1/2
Step-by-step explanation:
slope = m = (y2 - y1)/(x2 - x1) = (-2 - (-5))/(11 - 17) = 3/(-6) = -1/2
Answer:
Slope= [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
When you are looking for slope you should use this [tex]slope=m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] then just plug in what you already know.
[tex]y_{1}=-5\\y_{2}=-2\\x_{1}=17\\x_{2}=11[/tex]
Now we insert it in the formula and solve to get the slope...
[tex]\frac{-2-(-5)}{11-17}=\frac{3}{-6}=-\frac{1}{2}[/tex]