Answer:
a[1] = 100
a[n] = 1.05·a[n -1]
Step-by-step explanation:
The given terms do not have a common difference, but do have a common ratio. Each is 1.05 times the previous. This is expressed in a recursive relation as ...
a[1] = 100
a[n] = 1.05·a[n -1]
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate how many miles will he travel in 8 miles
Answer:
520
Step-by-step explanation:
260/4=520/8
Method 1: Cross Multiply
Method 2: Find GCF
A group of three undergraduate and five graduate students are available to fill certain student government posts. If four students are to be randomly selected from this group, find the probability that exactly two undergraduates will be among the four chosen.
Answer:
[tex]Pr = 0.4286[/tex]
Step-by-step explanation:
Given
Let
[tex]U \to\\[/tex] Undergraduates
[tex]G \to[/tex] Graduates
So, we have:
[tex]U = 3; G =5[/tex] -- Total students
[tex]r = 4[/tex] --- students to select
Required
[tex]P(U =2)[/tex]
From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
So, we have:
[tex]Total = ^{U + G}C_r[/tex]
[tex]Total = ^{3 + 5}C_4[/tex]
[tex]Total = ^8C_4[/tex]
[tex]Total = \frac{8!}{(8-4)!4!}[/tex]
[tex]Total = \frac{8!}{4!4!}[/tex]
Using a calculator, we have:
[tex]Total = 70[/tex]
The number of ways of selecting 2 from 3 undergraduates is:
[tex]U = ^3C_2[/tex]
[tex]U = \frac{3!}{(3-2)!2!}[/tex]
[tex]U = \frac{3!}{1!2!}[/tex]
[tex]U = 3[/tex]
The number of ways of selecting 2 from 5 graduates is:
[tex]G = ^5C_2[/tex]
[tex]G = \frac{5!}{(5-2)!2!}[/tex]
[tex]G = \frac{5!}{3!2!}[/tex]
[tex]G =10[/tex]
So, the probability is:
[tex]Pr = \frac{G * U}{Total}[/tex]
[tex]Pr = \frac{10*3}{70}[/tex]
[tex]Pr = \frac{30}{70}[/tex]
[tex]Pr = 0.4286[/tex]
Graph the function
Is it a, b, c or d?
Answer:
D
Step-by-step explanation:
(the line is a / shape, so the slope is positive)
(the line crosses the y axis at (0,-2))
(using the above information, we can conclude that the equation is y=2x-2)
or
slope = m = rise/run = 2/1 = 2
y=mx+b
y=2x+b
Choose any point on the line) (1,0)
0=2(1)+b
b=-2
y=2x-2
A solution of alcohol and water is 90% alcohol. The solution is found to contain 63 milliliters of alcohol. How many milliliters total (both alcohol and water) are in the solution?
Answer:
70 [milliliters]
Step-by-step explanation:
Since the solution consists of 90% alcohol, the 63 milliliters of alcohol must represent 90% of the entire solution. Let the solution have [tex]x[/tex] milliliters in total. We have the following equation:
[tex]0.9x=63[/tex]
Divide both sides by 0.9:
[tex]x=\frac{63}{0.9}=\boxed{70}[/tex]
Therefore, there are 70 milliliters in the solution.
Answer:
[tex]thank \: you[/tex]
What is the value of x
(X+40) (3x)
A. 20
B. 35
C. 60
D. 70
Answer: A. 20 is the answer.
Step-by-step explanation:
x+40 = 3x
or, 40 = 3x-x
or, 2x = 40
or, x = 40/2
so, x = 20
The Master Chief collects spiders and starfish. If his spiders have 8 legs and his starfish have 5 legs, how many starfish must he have, given that his spider/starfish collection totals 19 creatures and 116 legs
Answer:
12 starfish
Step-by-step explanation:
Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:
x + y = 19
5x + 8y = 116
Solve by elimination by multiplying the top equation by -8:
-8x - 8y = -152
5x + 8y = 116
Add these together and solve for x:
-3x = -36
x = 12
So, he has 12 starfish.
The total number of starfish is 12 starfishes
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of starfish be = x
Let the number of spiders be = y
The number of legs for spiders = 8
The number of legs for starfish = 5
So , the equation will be
The total number of legs for x starfish = 5x
The total number of legs for y spiders = 8y
The total number of creatures = 19
So , x + y = 19 be equation (1)
And ,
The total number of legs = 116
So , 5x + 8y = 116 be equation (2)
Now , from equation (1) , x = 19 - y
Substituting the value of equation (1) in equation (2) , we get
5x + 8y = 116
5 ( 19 - y ) + 8y = 116
95 - 5y + 8y = 116
95 + 3y = 116
Subtracting 95 on both sides , we get
3y = 21
Divide by 3 on both sides , we get
y = 7
So , the number of spiders is 7 spiders
Substituting the value of y in equation (1) , we get
x + y = 19
x + 7 = 19
Subtract 7 on both sides , we get
x = 12
Therefore , the value of x is 12
Hence , The total number of starfish is 12 starfishes
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ2
find the missing side lengths
Answer:
Step-by-step explanation:
Because it is a 45-45-90 triangle
b=5
a= 5[tex]\sqrt{2}[/tex]
PLEASEEEE HELLLLP MEEEE
Answer:
c. 20/21
Step-by-step explanation:
You just multiply straight
3×7 = 21
4×5 =20
21/20 <---- and it can't be reduced farther than this.
Answer:
C. ²¹⁄₂₀
Step-by-step explanation:
OKOKOK DON'T WORRY I'M HERE :)))
--
When multiplying fractions, you multiply the numerators together and then multiply the denominators together.
The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).
The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).
Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.
Hope this helped!!
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
Below is a histogram representing the test scores from Mrs. Smith's 3rd period Algebra class. Which set of scores below could be represented by this histogram?
Answer:
82,83,84,80,84,86,91,96,95,99,97,92
which equations have a leading coefficient of 3 and a constant term of -2?
Answer: the answer to this is 3x-2
Step-by-step explanation:
find the inequality represented by the graph
Answer:
First, find the function of the line:
slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{0-3}{0-4} =\frac{-3}{-4}=\frac{3}{4}[/tex]y-intercept = 0Therefore, the function is [tex]y=\frac{3}{4} x[/tex].
Since it's the area under the graph that's shaded(not ≥ or >) and the graphed line is dotted(not ≤ or ≥), then the inequality would be [tex]y<\frac{3}{4} x[/tex].
Write an inequality to describe the region represented on the number line.
H
-4 -3 -2 - 1 0 1 2 3 4
O x>-3
O x>-3.5
O x<-3
O x<-3.5
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required number line is not included in the question.
A general explanation is as follows:
An open circle means > or <
A closed circle means >= or <=
Take, for instance, the attached number line:
The open dot on -3 means >-3 or <-3
The arrow points to the right direction, means >-3 i.e. greater than -3
Hence, the inequality is:
[tex]x > -3[/tex]
16. Select the equation that has only one solution.
A. 8 x + 3 = 3 X + 8
B. 12 x = 12 x + 7
C.4 x + 11 = 11 + 4 x
D. 6 x + 20 = 6 x
Answer:
A is the answer...........
Explanation
8x+3=3x+8
8x-3x=8-3
5x=5
x=5/5
x=1
In how many years will the interest of a sum Rs 3600 at the rate of 5.5% per year be Rs 594.8?
Answer:
in 3.04 years the will give required intrest
Find m so that the equation msin²x+cos²x=m-1 has a solution on the interval (0;π/4)
msin²x+cos²x=m-1
since the interval are 0 and π/4
Therefore
msin²(0)+cos²(0)=m-1
m(0)+1=m-1
1=m-1
m=2
use π/4 now
msin²(π/4)+cos²(π/4)=m-1
m(1/2)+(1/2)=m-1
m+1=2(m-1)
m+1=2m-2
-m=-3
m=3
Therefore
m=2 or 3
A portion of the Quadratic Formula proof is shown. Fill in the missing statement. Statements Reasons x² + x + b 4ac 4a? b? 4a² Find a common denominator on the right side of the equation a 2a X? + b 2a b? =4ac 4a? Add the fractions together on the right side of the equation a b2 - 4ac x+ Rewrite the perfect square trinomial on the left side of the equation as a binomial squared 2a 4a 2 Take the square root of both sides of the equation Vb -4ac x+ b 2a + 4a b - 4ас X + 2a + 4a 4ac + 2a 4a 1o ano 4a
Answer:
The fourth option.
x + b/2a = +- sqrt((b^2 - 4ac)/(4a^2))
Step-by-step explanation:
(I will give brainliest!)
Solve for x using the distributive property
7(x-2)-3(x+3)=5(x-3)+x
Answer:
Step-by-step explanation:
7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis
7x -14 -3x -9 = 5x -15 +x , isolate like terms
7x -3x -5x -x = 14 +9 -15, combine like terms
-2x = 8, divide both sides by -2
x= -4
The recursive formula for a geometric sequence is: a = 4 an=an-1×3 What is the 3rd term of this sequence?
Answer:
36
Step-by-step explanation:
a1 = 4
an=an-1 *3
a2 = a1 *3 = 4*3 = 12
a3 = a2*3 = 12*3 = 36
The given figure shows a small garden. The shaded area is
reserved for planting flowers and the rest of the area is for
grass. Find the ratio of the area of the garden reserved for
planting flowers to the area reserved for grass.
Answer:
2 : 3
Step-by-step explanation:
We'll begin by calculating the area of the entire garden. This can be obtained as follow:
Length of garden (L) = 12 m
Width of garden (W) = 5 m
Area of entire garden (A) =?
A = L × W
A = 12 × 5
Area of entire garden is 60 m²
Next, we shall determine the area of the garden reserved for flower. This can be obtained as follow:
Length of flower garden (L₁) = 12 – 4
= 8 m
Width of flower garden (W₁) = 3 m
Area of flower garden (A₁) =?
A₁ = L₁ × W₁
A₁ = 8 × 3
A₁ = 24 m²
Next, we shall determine the area of the garden reserved for grass. This can be obtained as follow:
Area of entire garden (A) = 60 m²
Area of flower garden (A₁) = 24 m²
Area of grass garden (A₂) =?
A = A₁ + A₂
60 = 24 + A₂
Collect like terms
A₂ = 60 – 24
A₂ = 36 m²
Finally, we shall determine the ratio of the area of the garden reserved for flowers to the area reserved for grass. This can be obtained as follow:
Area of flower garden (A₁) = 24 m²
Area of grass garden (A₂) = 36 m²
Ratio of flower garden to grass garden = A₁ : A₂
= 24 : 36
= 24 / 36
= 2 : 3
Therefore, the ratio of the area of the garden reserved for flowers to the area reserved for grass is 2 : 3
Find the area of the triangle with one angle of 150 degrees, and one side 6 cm and the other 7cm.
(Sorry, I could not figure out how to upload the picture)
A. 10.5 cm²
B. 18.2 cm²
C. 12.1 cm²
D. 21 cm²
Step-by-step explanation:
here's the answer to your question
Answer these 3 questions and show how por favor! 39-says what is his age
Answer:
I dont know. sorry sorry
Factor the greatest common factor. 5xy4-20x2y3
Answer:
Step-by-step explanation:
The greatest common factor of 5 and -20 is 5
x: the greatest common factor is x
y: the greatest common factor is y^3
Answer: 5xy^3(y - 4x)
simplify 3/4×(4)1/3÷(3)1/4
Answer:
The answer is 1
Step-by-step explanation:
3/4×13/3÷13/43/4×13/4×4/13=1You are responsible to provide tennis balls for a tournament. You know that a ball bounces like new when it is dropped and it bounces 82% of the previous height. Because of budget restriction for the tournament you need to test some used balls to make sure they bounce like new tennis balls. You drop a ball and it bounces multiple times; each bounce reaches 82% the height of the previous height. a. Is this sequence geometric or arithmetic
Answer:
arithmetic
Step-by-step explanation:
because it bounced double
Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?
Answer:
Amira is currently 24 years old and Pam is currently 12 years old
Step-by-step explanation:
Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].
We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].
Therefore, we have a system of equations:
[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]
Substitute the first equation into the second one:
[tex]2p-9+p-9=18[/tex]
Combine like terms:
[tex]3p-18=18[/tex]
Add 18 to both sides:
[tex]3p=36[/tex]
Divide both sides by 3:
[tex]p=\frac{36}{3}=\boxed{12}[/tex]
Now substitute this into any of the equations (I'll choose the first):
[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]
Therefore, Amira is currently 24 years old and Pam is currently 12 years old.
As James bought his textbooks for classes one semester, he estimated the cost to the nearest ten dollars. He knew he could cover the cost up to $315. His math book cost $68.41, biology text was $105.35, literature text cost $72.49, and the AutoCAD text was $59.91. What rounded sum did James determine
Answer:
$310
Step-by-step explanation:
The first step is to add the costs of the textbook together :
$68.41 + $105.35 + $72.49 + $59.91 = $306.16
In order to round off to the nearest ten dollars, look at the units figure, if the number is greater or equal to 5, add 1 to the ten figure. If this is not the case, add zero. Replace the unit digit with zero
The unit digit is greater than 6, so 1 is added to the tens digit. The amount becomes $310
Simplify the following expressions:
a) (√3 +√7)^2
b) (√5 -√3)^2
c) (2√5 + 3√2)^2
1.) 10+2√21
2.) 8-2√15
3.) 38+2√10
solution to all the answers:
NUMBER 1:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√3 +√7)^2, then it should look like this: 3 + 2√21 + 7.
=> add the numbers: 10 + 2√21.
NUMBER 2:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√5 -√3)^2, then it should look like this: 5 - 2√15 + 3.
=> add the numbers: 8 - 2√15.
NUMBER 3:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (2√5 + 3√2)^2, then it should look like this: 20 + 12√10 + 18.
=> add the numbers: 38 + 12√10.
I HOPE THIS HELPED!!
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
-URGENT- please helppp-
Answer:
Last option. She didn't use the reciprocal.
Answer:
The second, third, and fourth
Step-by-step explanation:
When you multiply two fractions, you multiply the numerator and denominator, not add them. Also, when you divide by a fraction and want to turn it into multiplication, you multiply by the reciprocal, which she didn't do. Hope this helps!
