Answer:
Sample space = 36
P(sum of 6) = 5/36
Step-by-step explanation:
Number of faces on a dice = 6
The sample space, for a toss of 2 dice ; (Number of faces)^number of dice
Sample space = 6^2 = 6*6 = 36
Sum of numbers appearing on the dice = 6
The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5
Total possible outcomes = sample space = 36
Probability, P = required outcome / Total possible outcomes
P = 5 / 36
Probabilities are used to determine the chances of events
The given parameters are:
[tex]n=6[/tex] --- the faces of a six-sided die
[tex]r = 2[/tex] -- the number of dice
(a) The number of sample points
This is calculated as:
[tex]Sample = n^r[/tex]
So, we have:
[tex]Sample = 6^2[/tex]
Evaluate the exponent
[tex]Sample = 36[/tex]
Hence, the number of sample points is 36
(b) The probability that the sum of 6
See attachment for the sample space of the sum of two dice.
From the sample space, there are 5 outcomes where the sum is 6.
So, the probability is:
[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points
Divide 5 by 36
[tex]Pr = 0.1389[/tex]
Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389
Read more about probabilities at:
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Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
Given the function, calculate the following values:
Answer:
Step-by-step explanation:
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
Select the correct answer.
The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake,
M= log (I/I)
.Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
Answer:
[tex]M = \log(10000)[/tex]
Step-by-step explanation:
Given
[tex]M = \log(\frac{I}{I_o})[/tex]
[tex]I = 10000I_o[/tex] ---- intensity is 10000 times reference earthquake
Required
The resulting equation
We have:
[tex]M = \log(\frac{I}{I_o})[/tex]
Substitute the right values
[tex]M = \log(\frac{10000I_o}{I_o})[/tex]
[tex]M = \log(10000)[/tex]
The equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
Since the magnitude of an earthquake on the Richter sscale is M = ㏒(I/I₀) where
I = intensity of eartquake and I₀ = reference earthquake intensity.Since we require the magnitude when the intensity is 10,000 times the reference intensity, we have that I = 10000I₀.
Magnitude of earthquakeSo, substituting these into the equation for M, we have
M = ㏒(I/I₀)
M = ㏒(10000I₀./I₀)
M = ㏒10000
So, the equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
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A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.
Answer:
At most 3 calls: 64.7%
At least 3 calls: 57.7%
5 or more calls: 18.5%
Step-by-step explanation:
Please help!
Solve for x
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Answer:
x = 1
Step-by-step explanation:
The product of lengths to the two circle intercepts are the same for each secant.
7(7+9) = (8x)(8x+6x)
112 = 112x² . . . simplify
1 = x² . . . . . . divide by 112
x = 1 . . . . . . . take the square root (segment lengths are positive)
Question 4 4 pts Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: 5 years? 10 years? 486 months?
Answer:
Step-by-step explanation:
5 years
[tex]1500(1+\frac{.06}{12})^{12*5}=2023.275229[/tex]
10 years
[tex]1500(1+\frac{.06}{12})^{10*12}=2729.095101[/tex]
486 months:
[tex]1500(1+\frac{.06}{12})^{486}=16935.47074[/tex]
round those as you please
Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
Learn more about Arithmetic operations here:
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On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
At a store, 2 gallons of milk cost $6.
Which is the value of the ratio of dollars to gallons of milk?
0.33
per gallon
$3 per gallon
Answer:
B
Step-by-step explanation:
$3 per gallon
that is the procedure above
find all the missing measurement
Answer:
find all the missing measurementI need help with this
Answer:
Statement A is correct
Step-by-step explanation:
Statement A is correct: Model A1 (0.25) is more prefered than Model C3 (0.15)
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
The soil samples for the next field indicate that fertilizer coverage needs to be
greater. To achieve this, you need to increase flow rate. How would you achieve
this?
A. Increase speed to approximately 7.1 mph so that you cover the field more
quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more
slowly
D. Shift to second gear so that the engine speed slows
Answer:
A. Increase speed to approximately 7.1 mph so that you cover the field more.
Step-by-step explanation:
The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.
Solve the equation 10 + y√ = 14
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Answer:
y = 16
Step-by-step explanation:
Perhaps you want to solve ...
10 +√y = 14
√y = 4 . . . . . . subtract 10
y = 4² = 16 . . . square both sides
If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
If in 1 month you can make 6 carpets, how many days will it take for making 10 carpets?
Si en 1 mes puedes hacer 6 alfombras, ¿cuántos días se necesitarán para hacer 10 alfombras?
Step-by-step explanation:
6 carpets=1month
10 carpets=?
1month=31 days
10 /6*31
51
Step-by-step explanatio
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
What is the answer to this question in the picture
9514 1404 393
Answer:
[tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]
Step-by-step explanation:
It's pretty straightforward. You want ...
f(x) - g(x)
Substituting the given function definitions gives ...
[tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 12 cm and the width is 8 cm, how fast is the area of the rectangle increasing
Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];
the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and
[tex]\frac{dA}{dt}=72+56[/tex] so
[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]
There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balsa numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds for it being striped.
If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
What do we know?
We know that there are 15 billiard balls.
We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.
And the other 7 balls are striped.
Now we want to find the probability for a randomly selected ball to be a striped ball.
Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).
Then we have:
P = 7/15 = 0.467
That quotient is also what is called the "odds"
So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
If you want to learn more, you can read:
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MFP15017010 2021 Question 2 2.1 Calculate the following 2- and 3-digit numbers using strategic doubling: 34 2.1.2 340 2.13 277 214 00 (10) 2.15 500
Answer:
plz check ur school solution down.
Step-by-step explanation:
PLEASE HEP ME
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
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Answer:
TrueTrueStep-by-step explanation:
The center of dilation (point D) is a point that doesn't move. Any line not through that point will be moved to a parallel location when a dilation factor is applied.
Any line through the center of dilation will still go through the center of dilation. Its slope does not change, so the line will appear to be the same.
AB ║ A'B' — True
AD ≅ A'D' — True
_____
You can see these relationships in the attached figure.
help I was never taught how to do this im confused
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
determine a simplified expression
Answer:
For Task B: [tex]3x^4 - 2x^3[/tex]
Step-by-step explanation:
Given that Volume = l*w*h, we can plug in the values on the diagram, so we get the equation (3x-2)([tex]\frac{1}{2}x[/tex])([tex]2x^2[/tex]) = [tex](\frac{3}{2} x^2 - x)(2x^2) = 3x^4-2x^3[/tex]. Hope this helps!!!
1. One half of a number added to a second
number equals 4. One half of the first
number decreased by the second number
equals zero. Find the two numbers.
Answer:
(4, 2)
Step-by-step explanation:
½x + y = 4
y = 4 - ½x
½x - y = 0
½x - (4 - ½x) = 0
½x - 4 + ½x = 0
x = 4
y = 4 - ½(4)
y = 2
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
Absolute Value Equations
Answer:
4 is E, 5 is A
Step-by-step explanation:
4) Divide both sides by 5 to get |2x + 1| = 11, then solve for x to get 5 and -6.
5) Add 7 to both sides to get ½|4x - 8| = 10. Multiply both sides by 2 to get |4x - 8| = 20, then solve for x to get 7 and -3.