The probability that Ignatz rolls his first 5 before he rolls his second (not necessarily distinct) even number is: 13/32
Events:Define Event A: Rolling 5 before an even number.
Define Event B: Rolling an even number before a 5 (complementary event to event A).
Sample Space: - The total number of outcomes for rolling a die 5 times is [tex]6^5[/tex] (each roll has 6 possibilities).Favorable Outcomes for Event A:- We can achieve event A in various scenarios where Ignatz rolls a 5 before encountering an even number. Let's consider each case:Case 1: 5 in the first roll (1 way). Then, any other number (not 2, 4, or 6) in the remaining rolls (5 possibilities each).
Favorable outcomes: [tex]1 * 5 * 5 * 5 * 5.[/tex]
Case 2: 5 in the second roll (similar to case 1).
Favorable outcomes: [tex]5 * 1 * 5 * 5 * 5.[/tex]
We can continue using the same logic for cases where 5 appears in the third, fourth, or fifth roll.
Total Favorable Outcomes for Event A:Since there are multiple ways to achieve event A, we add the favorable outcomes from each case.Total Favorable Outcomes (A) = Favorable Outcomes (Case 1) + Favorable Outcomes (Case 2) + ... + Favorable Outcomes (Case 5)
= [tex]1 * 5^4 + 5 * 1 * 5^4 + 5^2 * 1 * 5^3 + 5^3 * 1 * 5^2 + 5^4 * 1 * 5[/tex]
Probability of Event A:Probability (A) = Favorable Outcomes (A) / Total Outcomes
[tex]= ( 1 * 5^4 + 5 * 1 * 5^4 + 5^2 * 1 * 5^3 + 5^3 * 1 * 5^2 + 5^4 * 1 * 5) / 6^5[/tex]
Probability of Event B (complementary event):Event B is the opposite of event A. Since events A and B cover all possibilities, their probabilities sum to 1.
Probability (B) = 1 - Probability (A)
Therefore, the probability of rolling a 5 before an even number (event A) is 1 - Probability (B).
an air traffic controller is tracking two planes. To start, playing a is at an altitude of 2814 ft and plan B is just taking off. Plan a is gaining altitude at 30.5 feet per second in playing day is gaining altitude at 80.75 feet per second. How many seconds will pass before the planes are on the same altitude
Answer:
56 seconds will pass.
Step-by-step explanation:
Because its right. :)
please give brainliest
Order the fraction from least to greatest.
2/3, 4/9, 5/6, 7/12
Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.
If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.
Splash of Color will always charge the least.
If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.
If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.
If it takes 3 hours to paint the rooms, both companies will charge the same amount.
Answer:
The correct statements are 1, 3, and 5.
Explanation:
Let's calculate the total cost for each company based on the given information:
For Interior Designs USA:
- Evaluation fee: $60.00
- Labor cost per hour: $35.00
- Total labor cost for 7 hours: $35.00/hour × 7 hours = $245.00
- Total cost = Evaluation fee + Total labor cost = $60.00 + $245.00 = $305.00
For Splash of Color:
- Labor cost per hour: $55.00
- Total labor cost for 7 hours: $55.00/hour × 7 hours = $385.00
Now, let's analyze the statements:
1. If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. - True. ($305.00 < $385.00)
2. Splash of Color will always charge the least. - False. In this case, Interior Designs USA charges less for 7 hours of work.
3. If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. - True. As we've seen, Splash of Color charges $55.00 per hour, while Interior Designs USA charges $35.00 per hour plus an initial fee.
4. If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. - False. Let's calculate:
- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 10 hours = $60.00 + $350.00 = $410.00
- Splash of Color: $55.00/hour × 10 hours = $550.00
Splash of Color charges $550.00 - $410.00 = $140.00 more, not $200. Therefore, this statement is false.
5. If it takes 3 hours to paint the rooms, both companies will charge the same amount. - False. Let's calculate:
- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 3 hours = $60.00 + $105.00 = $165.00
- Splash of Color: $55.00/hour × 3 hours = $165.00
They both charge $165.00, so this statement is true.
So, the correct statements are 1, 3, and 5.
Suppose a and b are 3x3 matrices, with det(a) = 5 and det(b) = 3.
a. det(2a) = ? 4 pts
b. det((ab)-1) = ?
kayla wrote a three-digit number.the value of the digit in the hundreds place is 6 hundreds. the digit in the tens place is 3 less than the digit in the hundreds place. sum of all three digital is 12.what is kayla number?
The area of a square garden is 98 meters squared. How long is the diagonal
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
Compare methods of solving linear equations and methods of solving linear inequalities. what do they have in common? what is different?
A miner descended 1500 feet into a mine. While in the mine, he then rose 1200 feet and then descended 850 feet. What was the miner's net gain or loss in altitude?
the table shows the low temperature in five cities on a winter day. which statement is true
A. it is warmer in Tacoma than in Roseville
B. it is colder in Roseville Than in Helena
C. It is warmer in Helena than in Fargo
D. it is colder in Tacoma than in Great Falls
What is "The sum of m and n"
Let f(x,y)=x2 −y2. find the gradient of f at the point (√2,1). sketch the level curve of f through this point, together with the gradient at that point. g
Answer:
[tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2 \hat{\j}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Differentiation
Partial DerivativesDerivative NotationGradient: [tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]
Gradient Property [Addition/Subtraction]: [tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x, y) = x^2 - y^2[/tex]
[tex]\displaystyle P(\sqrt{2}, 1)[/tex]
Step 2: Find Gradient
[Function] Differentiate [Gradient]: [tex]\displaystyle \nabla f(x, y) = \frac{\partial f}{\partial x} \bigg[ x^2 - y^2 \bigg] \hat{\i} + \frac{\partial f}{\partial y} \bigg[ x^2 - y^2 \bigg] \hat{\j}[/tex][Gradient] Rewrite [Gradient Property - Addition/Subtraction]: [tex]\displaystyle \nabla f(x, y) = \bigg[ \frac{\partial f}{\partial x}(x^2) - \frac{\partial f}{\partial x}(y^2) \bigg] \hat{\i} + \bigg[ \frac{\partial f}{\partial y}(x^2) - \frac{\partial f}{\partial y}(y^2) \bigg] \hat{\j}[/tex][Gradient] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \nabla f(x, y) = 2x \hat{\i} - 2y \hat{\j}[/tex][Gradient] Substitute in point: [tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2(1) \hat{\j}[/tex][Gradient] Simplify: [tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2 \hat{\j}[/tex]∴ the gradient of the given f(x, y) function is equal to <2√2, -2>.
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Topic: Multivariable Calculus
Unit: Directional Derivatives
rachel's necklace cost 20% more than Tammy's shoes. Bryan' s video game cost 30% more than Rachel's necklace. If Tammy's shoes cost $30.00, what did Brian's video game cost?
Answer:
46.80
Step-by-step explanation:
Pls brainly I need it so bad I spent 10 minutes of my time to solve this.
Find the distance between points M(6,16) and Z(-1,14) to the nearest tenth.
What's the range of 37000 and 45000
1.Find the coordinates of the midpoint of __ given that H (-1,3) and X (7,1).
HX
A.(3,1)
B (0,4)
C(-3,1)
D(-4,0)
2. Find the distance between the points R(0,5) and S(12,3). round the answer to the nearest tenth.
A 10.4
B 16
C 12.2
D 11.8
3. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85) what is the shortest possible distance for the trip?
A. 165 units
B. 170 units
C. 97 units
D. 169 units
Answer:
1. (3, 2)
2. Option C. 12.2
3. Option A. 165 units
Step-by-step explanation:
1. The midpoint of two coordinates (x₁, x₂) and (y₁, y₂) is calculate by,
[tex](x, y) = (\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2})[/tex]
⇒[tex](x, y) = (\frac{-1 + 7}{2},\frac{3 + 1}{2})[/tex]
Thus (x, y) = (3, 2)
Hence, none of given options are true.
2. The distance between two coordinates is calculate by,
[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
⇒ Distance = 12.16 ≈ 12.2 unit
Hence, option (C) is correct.
3. The distance between T(80, 20) and V(110, 85) is comparatively smaller than T(80, 20) and U(20, 60).
Using the Distance formula,
[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
Distance between T(80, 20) and V(110, 85) is 71.59 unit
and Distance between U(20, 60) and V(110, 85) is 93.41 unit
So, Airplane firstly go to point V from point T and then point U.
Total shortest distance = 71.60 + 93.40 = 165 unit.
Hence, option (A) is correct.
If there were a million cars in line, bumper to bumper, with a average length of 10.14 feet, how long would that line be in miles? (Round to the nearest mile)
Which equation has the same solution as 4-2(x-5)-x-19
The equation 3x - 4 = 2x + 7 has the same solution as 4 - 2(x - 5) = x - 19, with both solutions yielding x = 11.
Let's solve the equation step-by-step: 4 - 2(x - 5) = x - 19
First, expand the left side:Now, let's compare this solution to other given equations:
2(x + 5) = -8The equation with the same solution as 4 - 2(x - 5) = x - 19 is 3x - 4 = 2x + 7.
Complete question: Which equation has the same solution as 4 - 2(x - 5) = x - 19?
2(x + 5) = -83(x - 3) = 9x + 2 = 2x - 33x - 4 = 2x + 7jackson made 15 calls in 20 minutes. how many calls per minute did he make
Find the roc of the volume of a cube with respect to the length of its side s
The roc of the volume of a cube with respect to the length of its side s is 3s².
What is rate of change?
The rate of change of a function is the rate at which the output values change over the input value.
The rate of change of a function is one degree less than the actual function.
The volume of a cube is :
V = s³
The rate of change of volume V with respect to length a will be :
dV/ds = d(s³ )/ds
= 3s²
This means that, a cubic function will have a quadratic rate of change
Hence, The roc of the volume of a cube with respect to the length of its side s is 3s².
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Determine the effective rate for $1 for 1 year at 5.9% compounded quarterly.
Tim bought a pen for $2.25, a pencil for $0.59, a notebook for $6.49, and a highlighter for $1.49. He used a coupon that gave him $5.25 off his entire purchase. How much did he spend in total?
This number represents the number of times the base is used as a factor
The domain for f(x) and g(x) is the set of all real numbers. let f(x) = 3x + 5 and g(x) = x2. find g(x) − f(x). x2 − 3x − 5 3x3 − 5x2 3x2 − 5 x3 − 5
The mailman delivered a $22 check and 3 - $14 bills today. He also took back 1- $5 bill. What is the total in the mailbox?
Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row. He sees 8 trombone players. How many flute or trombone players does Ken see
Consider the graph of f(x)=1/x. Which functions result in a vertical compression? Check all that apply.
a. g(x)=1/3x
b. g(x)=3/x
c. g(x)= - 3/x
d. g(x)= - 1/3x
Answer:
A & D
Step-by-step explanation:
One tablet contains 575 grams of muscle relaxing medication. How many grams are in 3 1/2 tablets
What number is 49 less than 78
If a production line produces 50 mouse traps every 30 minutes over the course of a 10-hour work day with a half hour break for lunch how many mouse traps are made in a day