INFORMATION:
We know that:
- stack of mail consists of 8 bills, 10 letters, and 6 advertisements.
- One piece of mail is drawn at random and put aside. Then a second piece of mail is drawn.
And we must find P (both are letters)
STEP BY STEP EXPLANATION:
To find the probability, we need to know that we have two events. First, when one piece of mail is drawn at random and put aside and, second, when a second piece of mail is drawn.
These two events are dependent. If A and B are dependent events, P(A and B) = P(A) • P(B after A) where P(B after A) is the probability that B occurs after A has occurred.
So, first
- Probability of A (the first piece is letter)
[tex]P(A)=\frac{favorable\text{ }cases}{total\text{ cases}}=\frac{10}{24}[/tex]- Probability of B after A
Since A already occurred and one piece of the mail was drawn (a letter), now in total we would have 9 letter and 23 total pieces
[tex]P(B\text{ after }A)=\frac{9}{23}[/tex]Finally, replacing in the initial formula
[tex]P(A\text{ and }B)=\frac{10}{24}\cdot\frac{9}{23}=\frac{90}{552}=0.1630[/tex]Finally, the probability would be 0.1630
ANSWER:
P (both are letters) = 0.1630
Find the value of x.
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
Table A shows a proportional relationship
What is proportional relationship?
When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.
In the figure we are given 2 tables
We plot both the curve on the graph we get
Table A shows a linear relationship where are Table b Does not shows a proportional relationship
Hence Table A shows a proportional relationship
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Answer:
Step-by-step explanation:
Here are some ingredients for bolognaise sauce 400g of minced beef 800g of tomato sauce 300 ml stock 300ml red wine. julia has 300g of minced beef. how much of the other ingredients does she need
Answer:
Step-by-step explanation:
she would have to use 3/4 of the ingrediants to the 400g of minced beef.
tomato sauce would be 600g
stock would be 225g
and red wine would be 225g
The quantity of chopped tomatoes is 600 g, of stock is 225 ml, and of red wine is 225 ml if Julie only has 300 g of minced beef.
The ratio is the comparison of two quantities to determine how frequently one quantity obtains the other. It can be shown as a fraction between two numbers.
Quantity of minced beef = 400 g
Quantity of chopped tomatoes = 800 g
Quantity of stock = 300 ml
Quantity of red wine = 300 ml
Taking ratios of all the quantities, we get:
minced beef: chopped tomatoes:stock: red wine
= 400:800:300:300
= 100:200:75:75 ( Dividing by 4, as a common factor)
Multiplying the above ratio by three to make the quantity of minced beef 300 g
= 300:600:225:225
Thus, the quantity of chopped tomatoes is 600 g, the quantity of stock is 225 ml, and the quantity of red wine is 225 ml if Julie only has 300 g of minced beef.
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In a race, Kara ran eight- eighteenths of a kilometer and cycled sixteen-eighteenths of a kilometer. Estimate how many kilometers the race was in all.
a) 1/2 kilometer
b) 1 kilometer
c) 1 1/2 kilometers
d) 2 kilometers
Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.
What is addition of two fractions?To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.
Now, total distance in race
8/18 + 16/18
= (8+16)/18
= 24/18
= 4/3
= [tex]1\frac{1}{3}[/tex] kilometers
Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
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Wich is closest to the volume of the cone in cubic feet?
Therefore let us input the values to find the volume of the cone
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\pi r^2h \\ r=\frac{8}{2}=4\text{ ft} \\ h=9ft \\ \text{volume}=\frac{1}{3}\pi r^2h \\ \text{volume}=\frac{1}{3}\times3.14\times4^2\times^{}9 \\ \text{volume}=\frac{1}{3}\times3.14\times16\times9 \\ \text{volume}=\frac{452.16}{3} \\ \text{volume}=\text{ }150.72ft^2 \end{gathered}[/tex]The answer should be A.
150 14 Solve for x. Round to the nearest tenth. 63.5 54.1 3.6 74.9
The given triangle is a right angled triangle having the follwoing sides;
Hypotenuse = x (longest side)
Opposite = 14 (side facing the given acute angle)
Theta = 15 degrees
Using the SOH trigonometry identity;
sin 15 = opposite/hypotenuse
sin15 = 14/x
x = 14/sin15
x = 14/0.2588
x = 54.09
x is approximately equal to 54.1. Option B is coorect
The first equation should be multiplied by 7 and the second equation by -6.
Answer:
Step-by-step explanation:
Tom’s car has 1119 gallons of gas. If he uses 38 of the gas, how much gas does the car have left?
Answer:
1,081 gallons
Step-by-step explanation:
1,119 - 38 = 1,081
triangle RST had coordinates: R(-2, 1) S(-8, 2) T(-4, 5) Draw the translation of RST 8 units right and 4 units down on your recording sheet. what are 3 coordinates of R'A. R'(-3, 6)B. R'(0, -2) C. R'(6, -3) D. R'(4, 1)
Since the translation is 8 units right and 4 units down, we have to add 8 to the x coordinate and subtract 4 to the y coordinate.
R=(-2,1)
R' = (-2+8,1-4)= (6,-3)
R' = (6,-3)
Do You Like Guns N' Roses, If So, What Is Your Favorite Song?
Answer:golden hour by JVKE
Step-by-step explanation:
Raul estimated that a fish tank contained 20
gallons of water. He later found that the fish
tank had a 40-gallon capacity. Calculate his
error as a percent.
Answer: 50%
Step-by-step explanation:
The error percent of the fish tank is 50%
Error percent:
Error percent means the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. It is also known as the percent error is the relative error multiplied by 100.
The formula to calculate the error percent is
δ = |vA - vE|/vA x 100
δ = percent error
vA = actual value observed
vE = expected value
Given,
Raul estimated that a fish tank contained 20 gallons of water. He later found that the fish tank had a 40-gallon capacity.
Here we need to calculate the error percent.
According to the error percent formula,
In this question
The estimated value = 20 gallons
Actual value = 40 gallons.
Now, we have to apply the values on the formula, then we get,
P% = (40 - 20)/40 x 100
P% = 20/40 x 100
P% = 1/2 x 100
P% = 0.5 x 100
P% = 50.
Therefore, the error percent is 50%.
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solve for y, 3x−5y = 6
Answer:
y = [tex]\frac{3x -6}{5}[/tex]
Step-by-step explanation:
3x - 5y = 6 ( subtract 3x from both sides )
- 5y = - 3x + 6 ( multiply through by - 1 )
5y = 3x - 6 ( divide both sides by 5 )
y = [tex]\frac{3x-6}{5}[/tex]
What is (9 x 10^4) (6 x 10^-7)?
Answer:0.0008994
Step-by-step explanation:
Product of two rational no. is 1 , if one of them is ⁵/², then the other no. isa) ⅖b) -1 c) 0
Given:
Product of two numbers is 1.
The one number is 5/2.
Let the another number be x.
[tex]\begin{gathered} x\times\frac{5}{2}=1 \\ x=1\times\frac{2}{5} \\ x=\frac{2}{5} \end{gathered}[/tex]Answer: Option a) is correct. the other number is 2/5.
pulse rates of adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. what is the percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm? what percentage of adult females have pulse rates below 90 bpm?
The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%
The percentage of adult females have pulse rates below 90 bpm - 89.97%
a)
X ~ N ( µ = 74 , σ = 12.5 )
P ( 49 < X < 86.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 49 - 74 ) / 12.5
Z = -2
Z = ( 86.5 - 74 ) / 12.5
Z = 1
P ( -2 < Z < 1 )
P ( 49 < X < 86.5 ) = P ( Z < 1 ) - P ( Z < -2 )
P ( 49 < X < 86.5 ) = 0.8413 - 0.0228
P ( 49 < X < 86.5 ) = 0.8186 ≈ 81.86%
b)
X ~ N ( µ = 74 , σ = 12.5 )
P ( X < 90 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 90 - 74 ) / 12.5
Z = 1.28
P ( ( X - µ ) / σ ) < ( 90 - 74 ) / 12.5 )
P ( X < 90 ) = P ( Z < 1.28 )
P ( X < 90 ) = 0.8997 ≈ 89.97%
What is pulse rate ?
The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).
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PLEASE HELP NOW DUE AT 11 PM. Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. .
In these linear expressions one is equivalent which is 3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .
What are linear expressions?An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.
Alternatively pluging; we will see that none of the exponents can be greater than 1.
2x - 3(1.3x - 2.5) = 5.9x + 7.5
2x -3.9x + 7.5 = 5.9 + 7.5
-1.9x + 7.5 ≠ 5.9 + 7.5
thus linear expression is not equivalent.
3- 2( - 2.6x + 2.1) = 5.2x - 1.2
3 + 5.2x - 4.2 = 5.2x - 1.2
5.2x - 1.2 = 5.2x - 1.2
thus, linear expression is equivalent.
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3/4+(1/2+1/4) 2⋅2
NEED HELP.
Answer:
15/8 for exact form
1.875 for decimal form
And
1 and 7/8 for mixed number form
hope this helps you!
(also already in the simplest form :)
What is the value of x?
Answer:
x=62
Step-by-step explanation:
X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.
-Hope this helps
it is decided that this barrel must be painted pink and the barrel's surface area is requested in order to determine the amount of paint needed. what is the surface area of the barrel g
The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²
Missing data from the problem:
radius of the barrel = 0.4 meters
height of the barrel = 1.2 meters
The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:
A = 2. πr² + 2. πr.h
Where:
r = radius
h = height
Plug the parameters into the formula:
A = 2. π(0.4)² + 2. π(0.4).(1.2)
A = 13 m²
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8b^2 + 56b + 48 = 0
Solve for X
Answer:
b= -1, -6
Step-by-step explanation:
divide by common factor
then use x=- b+- sqrt b^2-4ac/2a
separate the equations and solve them
X=
//////////////////////////
Answer:
x = 15
Step-by-step explanation:
150+3x-15=180 because of same-side interior angles therorem.
Then, we solve the problem to get 15.
Hope this helped! :)
Given: ZADB = ZCBD ZABDZCDB m ZA= 3x + 15 mZC=8x-20 Find: x and m ZA A4 D B
Answer:
x = 7 , ∠ A = 36°
Step-by-step explanation:
since ∠ ADB ≅ ∠ CBD ( alternate angles )
and ∠ ABD ≅ ∠ CDB ( alternate angles )
then ABCD is a parallelogram
the opposite angles of a parallelogram are congruent , so
∠ C = ∠ A , that is
8x - 20 = 3x + 15 ( subtract 3x from both sides )
5x - 20 = 15 ( add 20 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Then
∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°
Answer: x = 7 and m∠A = 36
Step-by-step explanation:
Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB
This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C
⇒3x +15 = 8x - 20
⇒3x + 15 - 3x = 8x - 3x -20
⇒5x = 20 + 15
⇒x = 7
Now m∠A = (3X7) +15 = 36
When and where does the story The circuit take place?
Answer:
Mexico to the United States in 1947
Step-by-step explanation:
Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
The value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Find the rate at which the value of the car is depreciating
And
write an equation that models the depreciation of the value of the car
And
How much will the car be worth when it is 8 years old?
The equation of the car can be given as and the price of the car after 8 years is $4445.
What is an exponential function?
A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.
We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Let the original price of the car be [tex]P_{0}[/tex]
After two years the price of the car is $11200
Mathematically it can be given as
[tex]11200= P_{0}e^{2x}[/tex]
After 6 years the price of the car is $6100
Mathematically it can be given as
[tex]6100=P_{0}e^{6x}[/tex]
Dividing both equations we get,
[tex]1.83=e^{-4x}[/tex]
Which can also be written as
[tex]e^{4x}=0.54[/tex]
on solving we get,
x=-0.154
Hence the rate at which price of the car is dropping is
[tex]P=P_{0}e^{-0.154t}[/tex]
No we have to find the original price of the car
To do so we substitute t=2 in the equation
we get
11200=[tex]P_0e^{-0.308}[/tex]
On solving we get,
15240=[tex]P_0[/tex]
Now we find the price of the car after 8 years
P=15240·[tex]e^{-1.232}[/tex]
On simplifying we get
P=$4445
Hence the price of the car after 8 years will be $4445
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Find the equation of a line, in slope intercept form, that has a slope of 3 and passes through the point of (-4, 2).
Answer:
y=3x+14
Step-by-step explanation:
First find the point using slope point form.
y-y₁=m(x-x₁)
Put y value in for y₁, x value in for x₁ and slope in for m.
y-2=3(x+4)
Simplify
y-2=3x+12
Solve for y to get slope intercept form Y=mx+b
y=3x+14
What is the equation of a line that passes though the Point (3, -7) and has a slope of -2?
Answer:
y = - 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 7 ) into the partial equation
- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1
y = - 2x - 1 ← equation of line
A bag contains 4 blue and 6 white tokens. Two tokens are drawn from the bag one after another, without replacement. Find the probability that: the first is blue and the second is white.
Concept; Probability
Step1: The total number of tokens is
[tex]6\text{white +4 Blue}=\text{ 10 tokens}[/tex]let the probability of blue be P(B) and the probability of red be P(R)
The probability that the first is Blue is
[tex]\begin{gathered} P(B)=\frac{number\text{ of blue }}{total\text{ number of tokens}}=\frac{4}{10}=\frac{2}{5} \\ \end{gathered}[/tex]The probability the second is white without replacement is
[tex]P(R)=\frac{number\text{ of white}}{total\text{ token}}=\frac{6}{9}=\frac{2}{3}[/tex]Hence the combined probability of Blue and Red is
[tex]P(BR)=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]Therefore the probability that the first is blue and the second is white is 4/15
What’s the answer plss
The length of XY=19.894 cm when the angle XYZ=90° and angle YZX=61° and the length of hypotenuse=17.4 cm. Using the property of trigonometry, a=b.sinα/sinβ.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is Hypotenuse?The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
Here,
a=b.sinα/sinβ
=17.4·sin(90°)/sin(61°)
=19.89436 cm
≈19.9 cm
When the hypotenuse is 17.4 cm long and the angles XYZ and YZX are 90° and 61°, respectively, the length of XY is 19.894 cm. Using the trigonometric formula a=b.sinα/sinβ.
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an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?
If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute
Referring to the attached picture, the two triangles in a cone are similar. Hence,
r/h = 48/24
or
r = 2h.
The volume of the liquid is given by:
V = 1/3 . πr²h
Substitute r = 2h,
V = 1/3 . π(2h)²h = 4/3 . πh³
Take the derivative with respect to t
dV/dt = 4/3 . 3πh² . dh/dt
dV/dt = 4 . πh² . dh/dt
Substitute dV/dt = -40 and h = 10
-40 = 4 . π(10)² . dh/dt
dh/dt = - 0.0318 in./minute
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