Answer:
56.25%
Step-by-step explanation:
If John rolls first and Lucy rolls second, in order to find the probability that Lucy wins we need to multiply the probability that John's roll is less than 10 by the probability that Lucy's roll is less than 10. There are a total of 12 possible outcomes that can occur in a pair of dice, therefore John's probability of rolling less than a 10 would be [tex]\frac{9}{12}[/tex] which would also be the same probability of Lucy rolling smaller than a 10. Now we simply multiply this probability by itself...
[tex]\frac{9}{12} * \frac{9}{12} = \frac{81}{144}[/tex] or 0.5625
We can multiply this decimal by 100 to get the percentage probability
0.5625 * 100 = 56.25%
The probability of Lucy winning the game is 56.25%
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x^2 16y^2
Answer:
The answer is below
Step-by-step explanation:
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16
Solution:
Given that the ellipse has the equation: 4x² + 16y² = 16
let us make x the subject of the formula, hence:
4x² + 16y² = 16
4x² = 16 - 16y²
Dividing through by 4:
x² = (16 - 16y²)/4
x² = 4 - 4y²
Taking square root of both sides:
[tex]x=\sqrt{4-4y^2 }\\[/tex]
The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4xy
[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]
Therefore the length = 2x = 2√2, the width = 2y = 2/√2
Please someone help me!
9514 1404 393
Answer:
P = (8, 0)
Step-by-step explanation:
The coordinates of point P are the weighted average of the end points. The weights are the reverse of the segment divisions.
P = (2/5)A +(3/5)B
P = (2(-4, -6) +3(16, 4))/5 = (-8+48, -12 +12)/5 = (40, 0)/5
P = (8, 0)
PETS Each month Travis spends $20 for premium food$10 for treats $18 for grooming, and $3 for toys for his pet. Write an expression that could be used to determine the amount he spends on these items for his pet over a period of 12 months.
Answer:
$492 per year
Step-by-step explanation:
The first step we take towards solving this question is to add all the numbers we were given as money spent(excluding that of the month)
$20 + $10 + $18 + $3 = $41 per month
This means that a total of $41 was spent per month.
Going further, since we're told it's 12 months, we then multiply it by 12, and thus, we have
$41 * 12 = $492 per year
Therefore, the total money spent is $492 per 12 months, or per year
Please help, I will give brainliest, I am struggling badly.
Answer: y = 5/2x - 4
Step-by-step explanation:
the equation is y = ax + b (a ≠ 0)
because the slope of the line is 5/2 => a = 5/2
the line passes through (0; -4) => -4 = b
=> the equation is y = 5/2.x - 4
Gabe Amodeo, a nuclear physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution?
Answer:
You need two equations: one for solution amounts and one for alcohol amounts.
Step-by-step explanation:
90 = X + Y
45 = (0.6)/X + (0.3)Y
Here X = amount of 60 % solution and Y = amount of 30 percent solution. Note that percentages have been converted to decimal amounts in the second equation.
From here you have to solve two equations with two unknowns. Easiest to solve first equation for X = 90 - Y, then substitute into second equation. this get you one equation in one unknown. Solving you you will get
X = 30 liters and Y = 60 liters.
A 16-oz bottle of parmesan cheese costs $5.78, while an 8-oz bottle costs $3.97. Which is the better buy? Round
your answer to the nearest cent if necessary.
Answer:
The 16-oz bottle is a better buy
Step-by-step explanation:
Find the better buy by finding which one has a lower price per ounce:
Calculate the price per ounce of both bottles by dividing the cost by the number of ounces
5.78/16
= 0.36
3.97/8
= 0.5
Since 0.36 is smaller than 0.5, the 16 ounce bottle is a better buy.
Answer:
The 16-oz bottle of parmesan cheese is the better buy.
Step-by-step explanation:
It is the better buy because, if you compare the prices and the ounces, I say that the 16-oz is the best buy.
А 1 cm
B. 5 cm
C. 11 cm
D. 25 cm
5 is the answer
here we have hypoteaus and base
so by using pythagoreaus theorem
p^2 = h^2 - b^2
p^2 = 13^2 - 12^2
p^2 = 169 - 144
p^2 = 25
p = root under 25
p = 5
Answer:
5 cm
Step-by-step explanation:
A^2+B^2=C^2
12^2+B^2=13^2
144+B^2=169 (You have to subtract 144 from both sides to get B^2 by its self)
-144 = -144
B^2= 25 (To get rid of the square you have to find the square root)
Square root of 25 = 5cm
What is 2/5x6 equal to
Find the value of the power.
8^3 =
Answer
Answer:512
Step-by-step explanation:
Answer:
512
Step-by-step explanation:
8*8*8=512
Please answer number 4 please
Answer:
x < -2.5
Step-by-step explanation:
N/A
Give three examples of equations where there would be no solution
Answer:
1) 2x+1 = 2x-4
2) 6x+2=3(2x+1)
3) -4x -5=-2(2x)+2
Step-by-step explanation:
We need to give three examples of equations where there would be no solution.
First we will define equation with no solution.
If solving an equation you get the result as 3=5 but 3 is not equal to 5, so the equation has no solution.
Examples of equations where there would be no solution
1) 2x+1 = 2x-4
2x-2x=-4-1
0=-1 ( false)
So, the equation has no solution.
2) 6x+2=3(2x+1)
6x+2=6x+1
6x-6x=1-2
0=-2 (false)
So, the equation has no solution.
3) -4x -5=-2(2x)+2
-4x-5=-4x+2
-4x+4x=2+5
0=7 (false)
So, the equation has no solution.
Solve the equation
-3x - 5 =16
What does x =??
Answer:
x=-7
Step-by-step explanation:
[tex]x = 21 \div - 3 \\ x = - 7[/tex]
Answer: -7
Step-by-step explanation:
Move all terms that don't contain
x
x
to the right side and solve
How do the values of the 5s in 73.591 and 8.075 compare?
A.10
B.100
C.1,000
PLEAS HELP!
Answer:
100
i hope it helps
Answer:
100
Step-by-step explanation:
can someone show me the problems to 4/3 x 2/5 and 2/5 divided by 4/3
Answer:
8/15 and 3/10
37. Simplify to find x:
3-(4 X 3) = x
(483) - 7
Answer:
-0.003 x 2+.195 x -.483=0. -0.003x^2+.195x-.483=0 2,3,3,3,5,3,2,3,
Prime factors. 1000,200,1000
square root of (x-(65/2))2 is (x-(65/2))2/2 = (x-(65/2))1 = x-(65/2)
Step-by-step explanation:
−0.003 x 2+.195 x −.483=0. Enter an ... -0.003x^2+.195x-.483=0 ... {Left,Right}. 2, 3, 3, 3. 5, 3, 2, 3. Product of all. Prime Factors, 1000, 200, 1000 ... Step 7 : ... Note that the square root of (x-(65/2))2 is (x-(65/2))2/2 = (x-(65/2))1 = x-(65/2)
NEED HEP WILL GIVE BRAINLIEST IF YOU SOLVE ALL 3
Answer:
1) cant solve, you accidentally cropped out the bottom
2) ∠ABC=60°
3) x=25°
Step-by-step explanation:
1) cant solve, you accidentally cropped out the bottom. Let me know what the figure opposite the angle (5x-70) is and I can figure out the answer.
2)∠ABC=(45+15) (VERTICALLY OPPOSITE)
∠ABC=60°
(x=12.5°)
3) (x) + (3x-10) =90
4x -10 = 90
4x=100
x=25°
Determine which choice best shows the distributive property of multiplication.
Question 3 options:
1 × 4 = 4 × 1
1 × 1 = 1
1 × (4 × 6) = (1 × 4) × 6
1 × (4 + 6) = (1 × 4) + (1 × 6)
Question 5 (4 points)
(06.01)
Evaluate the expression 43+ (7 - 3) * 2. (4 points)
Blank 1:
Answer:
43+ (7 - 3) * 2 = 51
Step-by-step explanation:
43 + (7 - 3) x 2
First, you want to do what is in the parenthesis
43 + 4 x 2
Now, you want to multiply.
43 + 8
Next, you simplify.
51
You count 4 trucks and 11 cars in a college parking lot. Determine the fraction of cars to total number of vehicles in the lot. Identify the numerator and denominator of your fraction.
Answer:
Fraction of cars 4/15
Total number of vehicles 15
4 is the numerator and 15 is the denominator
Step-by-step explanation:
Select the correct answer.
Which equation is true for the value b= 10?
O A. 2(b + 4) = 16
OB.
2(b + 2) = 40
OC. 316 - 2) = 24
OD. 2(8 + b) = 42
O E. 3(b - 4) = 20
Answer:
C. 3(b - 2) = 24Step-by-step explanation:
b = 10
Substitute b in every equation below and compare the results
A. 2(b + 4) = 16
2(10 + 4) = 2(14) = 28 ≠ 16, incorrectB. 2(b + 2) = 40
2(10 + 2) = 2(12) = 24 ≠ 40, incorrectC. 3(b - 2) = 24
3(10 - 2) = 3(8) = 24, correctD. 2(8 + b) = 42
2(8 + 10) = 2(18) = 36 ≠ 42, incorrectE. 3(b - 4) = 20
3(10 - 4) = 3(6) = 18 ≠ 20, incorrectAnswer:
C. 3(b - 2) = 24..
Mr. Smith has a maximum of $50 to spend at a museum. A ticket to the museum costs $7. He
can spend p dollars to buy other things at the museum. Which inequality can be used to find
the possible values for p?
Answer:
Step-by-step explanation:
After buying the ticket, the amount with him = 50 - 7 = 43
p ≤ 50 - 7
p ≤ 43
Answer:
p≤ 43
Step-by-step explanation:
50-7=43
so now Mr.smith will have $43 to spend
p is less than or equal to 43
which equation is parrel to the equation y=3x-4
y=3x-8
y=4x+2
y=x-9
y=-1/3x+4
Answer:
Parallel means they have the same slope so, y=3x-8
The sum of the quotients of 25x2/5x and the quotient of 8x2/x is
A contractor has 12 gallons of paint which will cover 2,712 square feet. Which of the following rates best represents the relationships between the number of square feet and the number of gallons of paint?
A. 226 gallons of paint per square foot
B. 2,712 gallons of paint per square foot
C. 226 square feet per gallon of paint
D. 12 square feet per gallon of paint
What is f3 if f(x)=2x+1
Answer:
7
Step-by-step explanation:
F(x) =2x+1
f(x) =6+1
Caitlyn purchased a ring for her jewelry store at the wholesale price of $220 and marked up the price 35%. What is the list price of the ring?
Answer:
$297
Step-by-step explanation:
220 increase 35% =
220 × (1 + 35%) = 220 × (1 + 0.35) = 297
_ % of 4 is 7 someone pls help me
Answer:
175% of 4 is 7
Step-by-step explanation:
i hope this helps
Evaluate the expression when x = 3/4 and y= - 1/2: 2x +y
Answer:
1
Step-by-step explanation:
2(3/4)-1/2=
The 2 cancels out the 4 making it 3/2.
3/2-1/2=2/2
=1
What is the equation of the line through the points (2,3) and (4, 5)?
pls help, my teacher told me to translate this as an assignment so pls help.
th3f1r5t345y4551gnm3ntf0r411th35t9d3nt5.
and also this to. th3l45td4y0f5ch00l15601n6t0b31n4wh1l3.
answer key. y=7 e=3 s=5 a=4 9=u i=1 o=0 z=2 g=6 8=b.
Answer:
the first easy assignment for aii the students
the first day of school is go in to be in a while
Step-by-step explanation: