Answer:
Approximately [tex]0.19[/tex].
Step-by-step explanation:
The cards were drawn with replacement. Therefore, the probability of drawing a red card will be [tex](3 / 5)[/tex] at every one of the seven draws. The probability of not drawing a red card would be [tex](1 - (3/5)) = (2/5)[/tex].
One way to get three red cards out of the seven draws would be [tex]\verb!red!\; \verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!green![/tex]. That corresponds to a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex].
However, there are many other ways to get three red cards during the seven draws. For example:
[tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green![/tex], [tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green![/tex].[tex]\cdots[/tex].[tex]\verb!green!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!red!\; \verb!red![/tex].There are [tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} = 35[/tex] such ways in total to choose three draws out of seven draws.
These ways are mutually-exclusive. Each of these ways has a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex]. The probability for getting a red card on exactly three out of the seven draws would be:
[tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} \, (3/5)^3\, (1 - (3/5))^{7-3} \approx 0.19[/tex].
what is (9x+8)^2-54x+48y
Answer:
81x² + 90x + 48y + 64
Step-by-step explanation:
(9x+8)² = (9x+8)(9x+8) = 9x*9x + 9x*8 + 8*9x + 8*8 = 81x² + 72x + 72x + 64
= 81x² + 144x + 64
then:
(9x+8)² -54x+48y = (81x² + 144x + 64) -54x + 48y = 81x² + 90x + 48y + 64
A carpenter is building a rectangular shed with a fixed perimeter of 68 ft. What are the dimensions of the largest shed that can be built? What is its area?
The dimensions of the largest shed are _____ by _____.
The area of the largest shed is _____.
Answer:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
Step-by-step explanation:
Given that:
Fixed perimeter of the rectangular shed = 68 ft
To find:
The dimensions of the largest shed that can be built = ?
And
Area of the largest shed that can be built = ?
Solution:
First of all, let us have a look at the formula for perimeter of a rectangular shape shed:
Perimeter of a rectangle = 2 [tex]\times[/tex] (Length + Width)
68 = 2 [tex]\times[/tex] (Length + Width)
Length + Width = 34
The largest possible values are only in the case when the rectangle is a square.
i.e. Length = Width
Therefore values of length and width are:
Length = Width = [tex]\frac{34}{2} = 17\ ft[/tex]
Area of a square is given by the formula:
[tex]A = Side \times Side[/tex]
[tex]A[/tex] = 17 [tex]\times[/tex] 17 = 289 sq ft
The answer is:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
Andre performs a 90-degree counterclockwise rotation of Polygon P and gets Polygon P', but he does not say what the center of the rotation is. Can you find the center? Explain how you know.
Answer:
eefhhdfbhvfhfajfdhjk,nm?sorry dont knwo
Step-by-step explanation:
(a) Solve 5x - 2 = x + 8
Show clear algebraic working.
Answer:
Required Answer:-[tex]{:}\longrightarrow[/tex][tex]\sf 5x-2=x+8 [/tex]
interchange both sides[tex]{:}\longrightarrow[/tex][tex]\sf 5x-x=8+2 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 4x=10 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {10}{4}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {5}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=2.5 [/tex]
Write a division problem that has a quotient of 12.
At least one of the numbers you give must be a proper fraction. The other can be a proper fraction, whole number, or
improper fraction. Neither the dividend nor the divisor can be 12.
what is the minimum----------------------------------
Answer: A (-2,5)
Step-by-step explanation:
Select all sides lengths x for the missing side of abc
Can someone help me please
Answer:
What do you need to know?
Step-by-step explanation:
what is the value of b and c
Answer:
its 7
Step-by-step explanation:
Choose the expanded form of this number.
504,969
Answer:
Step-by-step explanation:
500,000+0+900+60+9
4x-3=2x+7 Someone Help Please
Answer:
x=5
Step-by-step explanation:
4x-3=2x+7
subtract 2x from both sides
2x-3=7
add 3 to both sides
2x=10
divide both sides by 2
x=5
Answer:
x = 5
Step-by-step explanation:
Original Equation:
4x - 3 = 2x + 7
Add 3 to both sides
4x = 2x + 10
Subtract 2x from both sides
2x = 10
Divide both sides by 2
x = 5
Hope this helps :)
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As I was sitting on a dock, I noticed that the wavelength of the waves were about 6 m long. The crest
of each wave would pass the front of the dock every 8 seconds. Find the frequency of the wave.
Answer:
IT IS C I BET YOU 6 AND 8
Step-by-step explanation:
The frequency of the wave is equal to: C. 0.125 Hertz
Given the following data:
Wavelength = 6 mTime period = 8 secondsTo determine the frequency of the wave:
A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.
Some of the characteristics associated with a wave are:
Speed.Amplitude.Wavelength.Time period.Frequency.Mathematically, the frequency of a wave is given by the formula:
[tex]Frequency = \frac{1}{Time\;period}[/tex]
Substituting the given parameters into the formula, we have;
[tex]Frequency = \frac{1}{8}[/tex]
Frequency = 0.125 Hertz
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2. The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.
Answer:
The length = x = 15 unitsThe width = x-5 = 10 unitsStep-by-step explanation:
Let 'x' be the length of a rectangle
As the width of a rectangle is 5 units less than the length.
so
width of rectangle will be = w = x - 5 units
Area = 150 square units
Using the formula
Area = length × width
[tex]150=\left(x\right)\left(x-5\right)[/tex]
[tex]150=x^2-5x[/tex]
[tex]x^2-5x=150[/tex]
Subtract 50 from both sides
[tex]x^2-5x-150=150-150[/tex]
[tex]x^2-5x-150=0[/tex]
[tex]\left(x+10\right)\left(x-15\right)=0[/tex]
if
[tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x+10=0\quad \mathrm{or}\quad \:x-15=0[/tex]
[tex]x=-10,\:x=15[/tex]
As length can not be negative. so
x = 15 units
Hence,
The length = x = 15 units
The width = x-5 = 15-5 = 10 units
An apple tree can grow about 400 apples. Jake says that 13 apple trees can grow about 6,000 apples. Do you agree? Explain.
Answer: No. Since 13×400=5,200, 13 apple trees can grow about 5,200 apples. Jake's estimate of 6,000 is much higher than 5,200.
Answer:
you answered it
Step-by-step explanation:
you put no blah blah blah
What is the domain of the relation?
Answer:
I am not certain but it's either the last one or second to last my bet is -4<x<4 but you can try I am not certain tho
At the end of a snow storm, Mia saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. Let SS represent the depth of snow on Mia's lawn, in inches, tt hours after the snow stopped falling. The table below has select values showing the linear relationship between tt and S.S. Determine the rate at which the snow is melting per hour.
Answer:
the snow per hour is
Step-by-step explanation:
um wait what chart theres no info to awnser this sorry you may delete this awnser :( but im letting ya know
Answer:
1.5 is the answer.
Step-by-step explanation:
Select all that apply.
A graph shows _____ in picture form.
variables
facts
color
statistics
sums
data
Answer:
Data
Step-by-step explanation:
Please help me ? Please
Answer:
Step-by-step explanation:
Which tables give sets of values that satisfy the linear function y = 2x – 6
How many five-symbol computer passwords can be formed using the letters A to J and the digits 3 to 6
Answer:
3354 ???
Step-by-step explanation:
i think thats right, have a good day! :)
plz give me brainliest if u can
Parallel to the line y=-3x + 5 passes through (-4,5)
Answer:
The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7
Step-by-step explanation:
Given equation of line is:
[tex]y = -3x+5[/tex]
General form of slope-intercept equation of line is:
[tex]y=mx+b[/tex]
Comparing both we get
m = -3
The slope of two parallel line sis equal.
Let m1 be the slope of line parallel to given line, then
m1 = -3
Putting in general form
[tex]y = -3x+b[/tex]
Putting (-4,5) in equation
[tex]5 = -3(-4) +b\\5 = 12+b\\b = 5-12\\b = -7[/tex]
Putting in the general form, we get
[tex]y = -3x-7[/tex]
Hence,
The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7
Kaylie and Juan are in a Dance-a-thon. Contestants rest for the same amount of time every hour. Kaylie rests for 22 minutes in 4 hours. How long did they rest in 28 hours? Find the unit rate.
Answer:
154 mins or 2 hour and 34 mins
Step-by-step explanation:
Step 1:
22 : 4 Ratio
Step 2:
22 : 4 = x : 28 Equation
Step 3:
4x = 616 Multiply
Step 4:
x = 616 ÷ 4 Divide
Answer:
x = 154
Hope This Helps :)
Let f(x) = 4x – 2 and g(x) = x + 1. Find the following function value.
(f - g)(-3)
Answer:
(f - g)(3) = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 4x - 2
g(x) = x + 1
Step 2: Find
Find (f - g)(x)
Substitute: (f - g)(x) = 4x - 2 - (x + 1)Distribute -1: (f - g)(x) = 4x - 2 - x - 1Combine like terms: (f - g)(x) = 3x - 3Find (f - g)(3)
Substitute: (f - g)(3) = 3(3) - 3Multiply: (f - g)(3) = 9 - 3Subtract: (f - g)(3) = 6Alexa and her children went into a movie theater where they sell bags of popcorn for $8 each and pretzels for $5 each. Alexa has $45 to spend and must buy a minimum of 6 bags of popcorn and pretzels altogether. If x represents the number of bags of popcorn purchased and y represents the number of pretzels purchased, write and solve a system of inequalities graphically and determine one possible solution.
One possible solution from the graph is selling 3 bags of popcorn and 4 bags of pretzel
What is inequality?
Inequality is the non equal comparison of two or more variables and numbers.
Let x represents the number of bags of popcorn purchased and y represents the number of pretzels purchased.
Hence:
8x + 5y ≤ 45 (1)
Also:
x + y > 6 (2)
One possible solution from the graph is (3, 4)
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–3t — 6t =
syplified
Answer:
-9t
Step-by-step explanation:
-3t -6t
using multiplication of signs
-×-=+
so add the numbers because they have the same
coefficient
-3-6= -9
so
-3t-6t=9t
There are 52 cards in a standard deck of cards, with four of each type of card: Ace ,2,3,4,5,6,7,8,9,10,Jack ,Queen ,King . Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction:
Answer:
The probabilitiy of pulling a seven is 1/13 or 7.69%
Step-by-step explanation:
Im not sure if you wanted just the probability of pulling a seven or if you wanted others as well but to find out the probability you take the total amount of cards, 52, then you take the total amount of 7's in the deck which is 4, one for each card type.
Therefore you get 4/52 or simplified to 1/13 by dividing by 4 on the numerator and the denominator.
The probability is defined as the ratio of favorable outcome to the total number of outcomes. The probability of getting a 7 out of deck of cards is 1 / 13.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
Given that,
The total number of cards = 52
The types of card present in a the deck = 4.
Suppose A be the event of selecting one 7 out of a deck of cards,
Then, the probability of event A can be given as,
P (A) = Number of 7's in the deck ÷ Total number of cards in the deck.
Since, there are four types of cards, the number of 7's in the card is 4.
Thus, P(A) = 4 / 52
=> P(A) = 1 / 13
Hence, the probability selecting one 7 out of a deck of cards is P(A) = 1 / 13.
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Anna is x years old and her sister, Jane is y years younger
What was the sum of their ages two years ago?
What will be the sum of their ages in 3 years?
How old was anna when Jane was born?
Answer:
Age of Anna = x years
Age of Jane i.e. Anna's sister = (x-y) years
a, What was the sum of their ages two years ago?
Solution,
Age of Anna two years ago = (x-2) years
Age of Jane two years ago = (x-y-2) years
Sum of their ages = x - 2 + x-y-2 = 2x - y -4
b. What will be the sum of their ages in 3 years?
Solution,
We have,
Present age of Anna = x years
Present age of Jane = (x-y) years
So,
Age of Anna after 3 years = (x+3) years
Age of Jane after 3 years = (x-y+3) years
Therefore,
Sum of their ages in 3 years = (x+3) +(x-y+3) = 2x - y+6
c. How old was Anna when Jane was born?
Solution,
Here,
According to question,
Jane is y years younger than Anna
So, Anna was y years when Jane was born.
[Suppose your age is 10 years and your brothers age is 14 years. You are 4 years younger than your brother. Also, his age was 4 years when you were born.]
P÷7 when p=42..................
help pls !! what is the value of K ?
A particle moves along a straight line with the equation of motion s = t^{5} - 2 t^{4} Find the value of t (other than 0 ) at which the acceleration is equal to zero.
Answer:
t = 8/5
Step-by-step explanation:
I'm assuming the equation given is the velocity of the particle
Derive the equation
[tex]5t^4 - 8t^3[/tex]
Set it equal to 0 & solve for t
[tex]0 = 5t^4 - 8t^3\\8t^3 = 5t^4\\8 = 5t\\\frac{8}{5} = t[/tex]
The value of time at which acceleration is zero is required.
The required value of [tex]t=1.2\ \text{s}[/tex]
The function of motion is
[tex]s=(t)^5-2t^4[/tex]
Differentiating with time we get velocity
[tex]s'=5t^4-8t^3[/tex]
Again differentiating with time we get acceleration
[tex]s''=20t^3-24t^2[/tex]
Now acceleration [tex]s''=0[/tex]
[tex]0=20t^3-24t^2\\\Rightarrow 20t^3=24t^2\\\Rightarrow t=\dfrac{24}{20}\\\Rightarrow t=1.2\ \text{s}[/tex]
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Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pints of ice cream, what is the greatest number of guests that Carly can serve?
Answer:
he can only serve 2
Step-by-step explanation: since 3.5 plus 3.5 is 7.0 if you add one more it turns to 7.0 plus 3.5 10.5 so the greatest he can serve is two people