Answer:
[tex]\frac{8}{17}[/tex] of fish in this aquarium are guppies.
Step-by-step explanation:
Let x be the number of guppies and y be the number of swordtails in the aquarium,
According to the question,
[tex]\frac{3}{4}\text{ of } x=\frac{2}{3}\text{ of }y[/tex]
[tex]\frac{3x}{4}=\frac{2y}{3}[/tex]
By cross multiplication,
[tex]9x=8y[/tex]
[tex]\implies \frac{x}{y}=\frac{8}{9}[/tex]
Thus, the ratio of guppies and swordtail fishes is 8 : 9
Let guppies = 8x, swordtail = 9x
Where, x is any number,
Since, the aquarium contains only two kinds of fish, guppies and swordtails,
So, the total fishes = 8x + 9x = 17x
Hence, the fraction of fish in the aquarium are guppies = [tex]\frac{\text{Guppies}}{\text{Total fishes}}[/tex]
[tex]=\frac{8x}{17x}[/tex]
[tex]=\frac{8}{17}[/tex]
To find what fraction of fish in the aquarium are guppies, you express the given relationship between the number of guppies and swordtails algebraically and solve for the number of guppies relative to the total number of fish, concluding that 8/17 of the fish in the aquarium are guppies.
If 3/4 of the number of guppies is equal to 2/3 of the number of swordtails, we can express this relationship using variables. Let G represent the number of guppies and S represent the number of swordtails in the aquarium. The given relationship can be written as (3/4)G = (2/3)S.
To find the fraction of fish that are guppies, we need to express G in terms of S first. By manipulating the equation, we multiply both sides by (4/3) to get G = (4/3)*(2/3)S = (8/9)S. This equation shows that the number of guppies is (8/9) times the number of swordtails.
Now, to find the total number of fish (T), we add the number of guppies and swordtails: T = G + S. Substituting the value of G from the equation above, we get T = (8/9)S + S = (17/9)S. The fraction of the total that are guppies is then G/T = [(8/9)S]/[(17/9)S] which simplifies to 8/17. Therefore, 8/17 of the fish in the aquarium are guppies.
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season.
What is Sandra’s expected value of points awarded for a race?
Integer Value Points Awarded Frequency
1-8 3 20
9-15 2 12
16-9 1 6
20 0 2
Answer:
2.25
Step-by-step explanation:
The total frequency is:
20 + 12 + 6 + 2 = 40
Calculate the probability of each score:
P(X=3) = 20/40 = 0.50
P(X=2) = 12/40 = 0.30
P(X=1) = 6/40 = 0.15
P(X=0) = 2/40 = 0.05
So the expected value is:
E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)
E = 2.25
In the figure below, if angle ZYX measures 23 degrees, then arc XY measures 45 degrees.
Answer:
FALSE
Step-by-step explanation:
Assuming ZY is a tangent, the measure of the arc will be twice the measure of the angle. If the angle ZYX is 23°, the measure of arc YX will be 46°.
What is the solution set of y = x2 + 2x + 7 and y = x + 7? A. {(0, 7), (-1, 6)} B. {(0, 7), (-7, 0)} C. {(0, 7), (1, 8)} D. {(-2, 0), (4, 0)}
Answer:
A.
Step-by-step explanation:
If
[tex]y=x^2+2x+7[/tex] AND
y = x + 7, then by the transitive property of equality:
[tex]x^2+2x+7=x+7[/tex]
We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:
[tex]x^2+x=0[/tex]
We can factor out the common x to get:
x(x + 1) = 0
which tells us by the Zero Product Property that either
x = 0 and/or x + 1 = 0 and x = -1
We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y
y = 0 + 7 so
y = 7 and the coordinate is (0, 7)
y = -1 + 7 so
y = 6 and the coordinate is (-1, 6)
Which is an exponential growth function?
A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find the value of the home after x years?
f(x) = 120,000(1.055x)
f(x) = 120,000(0.055)x
f(x) = 120,000(1.055)x
f(x) = [(120,000)(1.055)]x
Answer:
[tex]f(x)=120,000(1.055)^{x}[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
f(x) a home's value
x the number of years
a is the initial value
b is the base
b=(1+r)
r is the rate of grown
we have
a=$120,000
r=5.5%=5.5/100=0.055
b=1+0.055=1.055
substitute
[tex]f(x)=120,000(1.055)^{x}[/tex]
Answer:
It is In fact C. f(x) = 120,000(1.055)x
Step-by-step explanation:
Took this on Edg, it's right.
Help with these questions!
Step-by-step explanation:
An inscribed angle is half the arc angle.
m∠MNQ = 80°/2
m∠MNQ = 40°
The angle between two chords is the average of the arc angles.
m∠AMB = (80° + 85°) / 2
m∠AMB = 82.5°
Find the volume and surface area of the composite figure. Give four answer in terms of π.
Answer:
V = 99π in³; S = 81π in²
Step-by-step explanation:
Volume is that of a hemisphere of radius 3 in together with that of a cylinder of radius 3 in and height 9 in.
V = (2/3)πr³ +πr²h = (πr²)(2/3r +h)
= 9π(2 +9) = 99π . . . . in³
__
The area is that of a hemisphere, the side of the cylinder, and the circular bottom of the cylinder.
S = 2πr² +2πrh +πr² = πr(2r +2h +r)
S = 3π(6+18 +3) = 81π . . . . in²
Factor a number, variable, or expression out of the trinomial shown below:
6x2 – 12x + 9
A. 2(3x2 – 9x + 6)
B. 2(3x2 – 4x)
C. 3(2x2 – 4x + 3)
D. 3(2x2 – 4x + 9)
Answer:
C. 3(2x2 – 4x + 3)
Step-by-step explanation:
6x^2 – 12x + 9
We can factor out a 3
3(2x^2 -4x+3)
Answer:
c. 3(2x^2-4x+3)
Step-by-step explanation:
The numbers 6, 12, and 9 are all multiples of 3. Divide everything by three, move it to the outside. There are no more common factors between all 3 terms so the trinomial is completely factored. Hope this helped, if not then I apologize.
Please help me with this problem
Answer:
g(x) = -5x
Step-by-step explanation:
If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right. That point will be reflected through the x-axis to land at (1, -5). That means that the equation of the new line would be
g(x) = -5x
A reflection across the x -axis would have the opposite value of the output.
If the value is a positive value, the mirrored value would be a negative value.
The function of g(x) would be g(x) = -5x
MAJOORRRR HELPPPP!!!
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
It takes hours for the number of bacteria to increase to 300.
It takes 24 hours for the number of bacteria to increase to 300.
We have given that,
A scientist running an experiment starts with 100 bacteria cells.
These bacteria double their population every 15 hours.
Find how long it takes for the bacteria cells to increase to 300.
Use the formula, where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
[tex]P_0=100[/tex]
[tex]d=15[/tex]
What is the formula?[tex]P_t=P_02^{\frac{t}{d} }[/tex]
[tex]Pt=300=100\times2^{\frac{t}{15} }[/tex]
[tex]3=2^{\frac{t}{15}}[/tex]
[tex]\frac{t}{15} =1.6[/tex]
t=24
It takes 24 hours for the number of bacteria to increase to 300.
To learn more about the population increase visit:
https://brainly.com/question/11608113
#SPJ2
Finley's mother bought soda for her slumber party that has 10 people. Her mother bought 6 liters of soda. How many milliliters of soda can each child have?
Answer:
Step-by-step explanation:
5/3lit
Answer:young boy
Step-by-step explanation:two two
Solve the system of equations.
6d + 3f = 12
2d = 8 - f
a. d= 3, f = 2
b. d = 3, f = 14
c. no solution
d. infinite solutions
Answer:
c. no solution
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Multiply the second equation by 3
3*2d = 3(8-f)
6d = 24-3f
Substitute into the first equation for 6d
(24-3f) +3f = 12
Combine like terms
24 =12
This is never true, so there are no solutions
Answer:
c. No Solution.
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Rearranging the second equation:
2d + f = 8 Multiply this equation by 3:
6d + 3f = 24
Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.
Figure ABCD is a parallelogram.
5x + 3
What is the value of x?
Answer:
x=7
Step-by-step explanation:
Since this is a parallelogram, you can say that the 5x+3 will equal to 38 in this situation. 38-3 =35.
[tex]\frac{35}{5} \\\\x=7[/tex]
So the answer is 7
In your drawer you have 10 white socks, 6 black socks, 4 brown socks and 2 blue socks. Your roommate is still asleep, and you cannot turn the light on while you get dressed. You reach in blindly and grab two socks. What is the probability of pulling out a matching pair of black socks?
Answer: Required probability is,
[tex]\frac{36}{231}[/tex]
Step-by-step explanation:
Given,
White socks = 10,
Black socks = 6,
Brown socks = 4,
Blue socks = 2,
Total socks = 10 + 6 + 4 + 2 = 22,
Thus, the total ways of choosing any 2 socks = [tex]^22C_2[/tex],
Now, the ways of choosing a black socks = [tex]^6C_1[/tex]
Thus, ways of choosing a pair of black socks = [tex]^6C_1\times ^6C_1[/tex]
Hence, the probability of pulling out a matching pair of black socks
= [tex]\frac{^6C_1\times ^6C_1}{^{22}c_2}[/tex]
= [tex]\frac{36}{231}[/tex]
Natasha places an online order for plate holders to display her antique plates. She chooses a specific site because it has a promotional offer of 15% off on all purchases. She orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each. There is no sales tax on her purchase, but she must pay a flat rate of $5.35 for shipping and handling. What is the total of Natasha?s online purchase?
Answer:
Total online purchase is $26.473 .
Step-by-step explanation:
As given
Natasha places an online order for plate holders to display her antique plates.
Natasha orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each.
Thus
Total purchase of Natasha = Number of large holders × Cost of each large holder + Number of medium holders × Cost of each medium holder + Number of small holders × Cost of each small holder .
Put all the values in the above
Total purchase of Natasha = 3 × $4.95+ 2 × $3.25 + 2 × $1.75
= $14.85 + $6.5 + $3.5
= $ 24.85
As given
Site has a promotional offer of 15% off on all purchases.
15% is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Discount amount = 0.15 × Total purchase of Natasha .
= 0.15 × $24.85
= $ 3.7275
Thus
Total purchase of Natasha after discount = Total purchase of Natasha - Discount amount .
= $24.85 - $3.7275
= $ 21.1225
As given
Natasha must pay a flat rate of $5.35 for shipping and handling.
Thus
Total online purchase of Natasha = Total purchase of Natasha after discount + Flat rate for shipping and handling .
Total online purchase of Natasha = $21.1225 + $5.35
= $ 26.4725
= $26.473 (Approx)
Therefore the total online purchase is $26.473 .
Answer:
the order Natasha places is as follows;
3 large holders - $4.95 each - 4.95*3 = 14.85
2 medium holders - $3.25 each - 3.25*2 = 6.5
2 small holders - $1.75 each - 1.75*2 = 3.5
Total value for purchases is - 14.85 + 6.5 + 3.5 = 24.85
she gets 15% for all purchases therefore she has to pay only 85% of the purchase value
$24.85 * 85% = $21.1225
She has to pay an additional $5.35 for shipping and handling
therefore the total amount she has to pay is = 21.1225 + 5.35
total amount = 26.4725 this rounded off to second decimal place,
correct answer
C - $26.47
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
a.
a^2 + b^2 = c^2
The legs are a and b. c is the hypotenuse.
Let a = 6x + 9y; b = 8x + 12y; c = 10x + 15y
The equation is:
(6x + 9y)^2 + (8x + 12y)^2 = (10x + 15y)^2
b.
Now we square each binomial and combine like terms on each side.
36x^2 + 108xy + 81y^2 + 64x^2 + 192 xy + 144y = 100x^2 + 300xy + 225y^2
36x^2 + 64x^2 + 108xy + 192xy + 81y^2 + 144y^2 = 100x^2 + 300xy + 225y^2
100x^2 + 300xy + 225y^2 = 100x^2 + 300xy + 225y^2
The two sides are equal, so it is an identity.
Answer:
see below
Step-by-step explanation:
a The pythagorean theorem is a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + b^2 = c^2
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
b solve
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
(6x+9y)(6x+9y) + (8x+12y)(8x+12y) = (10x + 15y)(10x+15y)
Factor out the common factors
3(2x+3y)3(2x+3y) + 4(2x+3y)4(2x+3y) = 5(2x+3y)5(2x+3y)
Rearrange
9 (2x+3y)^2 +16 (2x+3y)^2 = 25(2x+3y)^2
Divide each side by(2x+3y)^2
9 (2x+3y)^2/ (2x+3y)^2 +16 (2x+3y)^2/(2x+3y)^2 = 25(2x+3y)^2/(2x+3y)^2
9 + 16 = 25
25=25
This is true, so it is an identity
An elevator starts at the main floor and goes up 8 floors. It then goes back fown 5 floors. What integer represents elevator final position with respect to the main floor?
Answer:
integer 3 represents elevator final position with respect to the main floor.
Step-by-step explanation:
Given : An elevator starts at the main floor and goes up 8 floors. It then goes back down 5 floors.
To find : What integer represents elevator final position with respect to the main floor.
Solution : We have given
Elevator starts at the main floor and goes up floors = + 8 ( for up).
Then goes back down floor = - 5 ( - sign for down).
Final position : 8 - 5 = 3 .
It will reach at 3 floor from the main floor .
Therefore, integer 3 represents elevator final position with respect to the main floor.
BRAINLIEST HURRY!
the griffins bought a netbook for$250.if the small computer depreciates at a rate of 25%a year,what will it be worth afer 3 years
Answer:
[tex]\$105.47[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$250\\r=25\%=25/100=0.25\\x=3\ years[/tex]
substitute
[tex]V=250(1-0.25)^{3}[/tex]
[tex]V=250(0.75)^{3}[/tex]
[tex]V=\$105.47[/tex]
Answer and Step-by-step explanation:
After three years the worth of it will be [tex]$105.47[/tex]
We know that each year, it's worth 75% of what it was, giving us :
[tex]=0.75*W[/tex] (Note that "W" means "Worth")
Now we calculate it in three years time so,
The first year is :[tex]250*0.75 = $187.50[/tex]
The second year is :[tex]187.5*0.75 = $140.625[/tex]
The third year is :[tex]140.625*0.75 = $105.47[/tex]
Now, we have our answer :
After three years time the worth of it is [tex]$105.47[/tex]
The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side
Answer:
(7.5-2.1) /2
If the shortest side measures 2.1 m.
7.5-2.1 =5.4. Then divide by 2 each side is 2.7m
Answer:
The equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
Step-by-step explanation:
Perimeter of the isosceles triangle = 7.5 m
Length of the shortest side = 2.1 m
Let the length of each of the other sides of the triangle = x meter
Then the equation for the perimeter of the triangle becomes:
Sum of 3 sides f the triangle = 7.5 m
=> 2*x + 2.1 = 7.5
=> 2*x = 7.5 - 2.1 = 5.4
=> x = 5.4/2 = 2.7 m
So the relevant equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
8. In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 28 vowels and 12 consonants, what is the probability you will choose a consonant and then a vowel?
Answer:
The probability that you will choose a consonant and then a vowel is 0.21....
Step-by-step explanation:
Total no of tiles = 28 + 12 = 40
First you should choose a consonant = 12/40
Second you should choose a vowel = 28/40
So the probability you choose a consonant and then a vowel:
= 12/40 * 28/40
=336/1600
=0.21
So the probability that you will choose a consonant and then a vowel is 0.21....
What are the discontinuity and zero of the function f(x) = x^2+5x+4/x+4
Answer:
The zeros of our function f is at x=-1.
The discontinuity is at x=-4.
These are correct if the function is [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] .
Please let know if I did not interpret your function correctly.
Step-by-step explanation:
I imagine you mean [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] but please correct me if I'm wrong.
The zero's of a rational expression occur from it's numerator.
That is, in a fraction, the only thing that makes that fraction 0 is it's numerator.
So we need to solve [tex]x^2+5x+4=0[/tex] for x.
The cool thing is this one is not bad to factor since the coefficient of x^2 is 1. When the coefficient of x^2 is 1 and you have a quadratic, all you have to do is ask yourself what multiplies to be c and adds to be b.
[tex]x^2+5x+4[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=5,c=4[/tex].
So we are looking for two numbers that multiply to be c and add to be b.
We are looking for two numbers that multiply to be 4 and add to be 5.
Those numbers are 1 and 4 since 1(4)=4 and 1+4=5.
The factored form of [tex]x^2+5x+4[/tex] is [tex](x+1)(x+4)[/tex].
So [tex]x^2+5x+4=0[/tex] becomes [tex](x+1)(x+4)=0[/tex].
If you have a product equals 0 then at least one of the factors is 0.
So we need to solve x+1=0 and x+4=0.
x+1=0 when x=-1 (subtracted 1 on both sides to get this).
x+4=0 when x=-4 (subtracted 4 on both sides to get this).
The zeros of our function f is at x=-1 and x=-4.
Now to find where it is discontinuous. We have to think 'oh this is a fraction and I can't divide by 0 but when is my denominator 0'. If the value for the variable is not obvious to you when the denominator is 0, just solve x+4=0.
x+4=0 when x=-4 (subtracted 4 on both sides).
So we have a contradiction at one of the zeros so x=-4 can't be a zero.
The discontinuity is at x=-4.
Answer:
This function is discontinuous at x = 4, and has a zero at x = -1.
Step-by-step explanation:
If x = -4, the denominator will be zero and thus the function will be undefined. Thus, the discontinuity is at x = -4.
To find the zero(s): Set the numerator = to 0, obtaining
x^2+5x+4 = 0. Factoring this, we get (x + 4)(x + 1) = 0. Thus, we have a zero at x = -1.
Notice that f(x) can be rewritten as
x^2 + 5x + 4 (x+4)(x+1)
f(x) = -------------------- = ---------------- = x + 1 for all x other than x = -4.
x + 4 (x+4)
This function is discontinuous at x = 4, and has a zero at x = -1.
What is the product of (3a + 2)(4a2 – 2a + 9)?
Answer:
12a^3 + 2a^2 + 23a + 18
Step-by-step explanation:
Please use the " ^ " symbol to represent exponentiation: 4a^2 – 2a + 9.
Now carry out the multiplication as follows:
First, multiply each term in 4a^2 – 2a + 9 by 3a: 12a^3 - 6a^2 + 27a.
Next, multiply each term in 4a^2 – 2a + 9 by 2: 8a^ 2 - 4a + 18.
Now combine like terms:
12a^3 - 6a^2 + 27a
8a^ 2 - 4a + 18
---------------------------------
12a^3 + 2a^2 + 23a + 18
Which graph shows an even function?
Answer:
A.Step-by-step explanation:
The graph of even function is symmetrical about the y-axis.
The graph of odd function is symmetrical about the origin.
A. even
B. odd
C. odd
D. neither
(look at the picture)
Answer:
I would be A
Step-by-step explanation:
It has symmetry across the y axis
MAJOR HELP!
Imagine you are at home watching television. You are sitting 6 feet away from your TV which is hung on the wall and the top of it is 8 feet off the ground. Which of the following functions correctly represents the angle θ that you make with the top of your television?
Answer: Option A
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Step-by-step explanation:
We can model the situation by means of a right triangle.
Where the angle [tex]\theta[/tex] is the angle that you make with the top of the TV.
Then the horizontal distance of 6 feet is the adjacent side and the vertical distance of 8 feet is the opposite side to the angle the.
By definition of the [tex]tan(\theta)[/tex] function we know that:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Therefore:
[tex]tan^{-1}(\frac{8}{6})=\theta[/tex]
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Answer:
CORRECT
Step-by-step explanation:
CAN SOMEONE HELP ME WITH THIS MATH QUESTION ITS ABOUT TRANSLATION
Answer:
(- 4, 1 )
Step-by-step explanation:
A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.
B = (- 5, 4 ), thus
B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )
[tex]B=(-5,4)\\\\B'=(-5+1,4-3)\\B'=(-4,1)[/tex]
What is the solution of the equation x2 − 12x = 8?
Answer:
x = 12.63 or x= -0.63
Step-by-step explanation:
From my understanding the question is x² - 12x = 8
This will be solved through a quadratic equation formula.
Step 1: Form a quadratic equation
x² - 12x = 8
x² - 12x - 8 = 0
Step 2: Apply the quadratic formula
a = 1, b = -12, c = -8
x = -b±√b²-4ac
2a
x = -(-12)±√(-12)²-4(1)(-8)
2(1)
Step 3: Find the value of x
x = 12±4√(11
2
x = 12+4√(11) or x = 12-4√(11)
2 2
x = 12.63 or x= -0.63
!!
n a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ____$. If one more $20 bill and one more $10 bill are added to the bag, the expected value will change to _____$.
Answer:
Initial expected value = 7.3 $
If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $
Step-by-step explanation:
a) Total number of bills = 2 + 1 + 4 + 3 = 10
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3[/tex]
Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$
b)If one more $20 bill and one more $10 bill are added to the bag
Total number of bills = 3 + 2+ 4 + 3 = 12
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25[/tex]
Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$
Answer:
$7.30 for the first one and $8.58 for the second one
Step-by-step explanation:
ANSWER FOR PLATO
PLEASE HELP MEOWT!!!
Rewrite sin^(4)xtan^(2)x in terms of the first power of cosine.
Step-by-step explanation:
[tex] { \sin(x) }^{4} { \tan(x) }^{2} [/tex]
[tex] { \sin(x) }^{4} \frac{ { \sin(x) }^{2} }{ { \cos(x) }^{2} } [/tex]
[tex] \frac{ ({ {1 - \cos(x) }^{2} })^{3} }{ { \cos(x) }^{2} } [/tex]
hopefully this helps, I'm rusty with my trig identities
Answer:
sin⁴(x)tan²(x) = (10 -15cos(2x) +6cos(4x) -cos(6x))/(16(1 +cos(2x))
Step-by-step explanation:
The relevant identities are ...
[tex]\sin^4{x}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\\\\\tan^2{x}=\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\\cos{(a)}\cos{(b)}=\dfrac{\cos{(a+b)}+\cos{(a-b)}}{2}[/tex]
Then your product is ...
[tex]\sin^4{(x)}\tan^2{(x)}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\cdot\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\=\dfrac{3-4\cos{(2x)}+\cos{(4x)}-3\cos{(2x)}+4\cos^2{(2x)}-\cos{(4x)}\cos{(2x)}}{8(1+\cos{(2x)})}[/tex]
Collecting terms and using the identity for the product of cosines, we get ...
[tex]=\dfrac{3-7\cos{(2x)}+\cos{(4x)}+4\dfrac{1+\cos{(4x)}}{2}-\dfrac{\cos{(6x)}+\cos{(2x)}}{2}}{8(1+\cos{(2x)})}\\\\=\dfrac{10-15\cos{(2x)}+6\cos{(4x)}-\cos{(6x)}}{16(1+\cos{(2x)})}[/tex]
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
Rx-axis (P) is (-4 , 1)
Step-by-step explanation:
* Lets revise the reflection
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
∵ The point P is (-4 , -1)
∵ Rx-axis (P) means reflect point P across the x-axis
∵ The reflection of a point (x , y) across the x-axis is (x , -y)
- That means we will change the sign of the y-coordinate of point P
∵ P = (-4 , -1)
∴ The y-coordinate of point P is -1 will change to 1
∴ The image of point P after reflection is (-4 , 1)
* Rx-axis (P) is (-4 , 1)
Answer:
P is -4 , 1
Step-by-step explanation:
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily. The amount per $1.00 is 1.221386. What is the interest earned to the nearest cent?
Answer:
The total interest earned is $1,439.
Step-by-step explanation:
Consider the provided information:
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily.
Now, Use the formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where, A is the total amount (after adding interest), P is the principal (investment or loan), r is the interest rate, n is compound, and t is the time (in years).
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=6500(1+\frac{0.05}{365} )^{4(365)}[/tex]
[tex]A=6500(1.00014)^{1460}[/tex]
[tex]A=6500(1.22139)[/tex]
[tex]A=7939.00918[/tex]
Therefore total interest earned is:
$7,939.00 - $6500 = $1,439.00
Hence, interest earned is $1,439.
Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school:
What is the minimum number of at-the-door tickets she needs to sell to make her goal?
A,333
B.334
C.66
D.67
Answer: The answer would be 333
Step-by-step explanation: Hope this was helpful
To make at least $5,000, Anna must sell a minimum of 200 at-the-door tickets priced at $25 each. This is the minimum required, but the venue's capacity allows for selling up to 400 tickets to potentially exceed the fundraising goal.
Explanation:The question asks us to calculate the minimum number of at-the-door tickets Anna needs to sell to meet the fundraiser target of at least $5,000, given the constraints of the venue capacity and the ticket prices. This can be solved by first identifying the total amount needed to be raised and then calculating the number of at-the-door tickets needed if no pre-sale tickets are sold.
Since at-the-door tickets sell for $25 each, we divide the total amount Anna wants to raise ($5,000) by the price of each at-the-door ticket:
$5,000 ÷ $25 = 200 tickets
This means Anna will have to sell at least 200 at-the-door tickets to raise $5,000. However, the venue limits the capacity to 400 people, and it is not specified how many pre-sale tickets are sold. To ensure reaching the target, assuming no pre-sale tickets are sold, Anna should aim to sell all 400 tickets at the door. Selling any fewer at the door would require pre-sale tickets to make up the difference to reach the $5,000 target.
Therefore, the minimum number of at-the-door tickets Anna needs to sell to reach the $5,000 goal is 200, although to fully utilize the venue's capacity and potentially exceed the target, she can sell up to 400 tickets at the door.
Learn more about Minimum Ticket Sales here:https://brainly.com/question/28454838
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