You roll a 20-sided die and a 6-sided die. What is the probability that the sum of the dice is less than 5?
1 answer:
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Answer:
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Step-by-step explanation:
Given - Ted and Jude are each saving money each month. After x months, the amount of money, in dollars, that Ted has saved is represented by the
equation T = 40x, and the amount of money that Jude has saved is represented by the equation J = 60x.
To find - Choose all of the statements that are true.
A. Each month, Jude saves two-thirds as much money as Ted saves.
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
C. The amount of money Jude saves each month is $20 more than the amount Ted saves each month.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Proof -
Given that,
After x months,
Ted saved the amount of money, T(x) = 40x
Jude saved the amount of money, J(x) = 60x
Now,
In 1 month,
Ted saved money, T(1) = 40(1) = 40
Jude saved money, J(1) = 60(1) = 60
So,
In 1st month, Jude saved money 20 more than Ted saved.
Now,
In 2 month,
Ted saved money, T(2) = 40(2) = 80
Jude saved money, J(2) = 60(2) = 120
So,
In 2nd month, Jude saved money 40 more than Ted saved.
Now,
In 3 month,
Ted saved money, T(3) = 40(3) = 120
Jude saved money, J(3) = 60(3) = 180
So,
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option C is incorrect
Because
In 1st month, Jude saves is $20 more than the amount Ted saves
In 2nd month, Jude saves is $40 more than the amount Ted saves
Now,
In 1st month,
Ted saves = 40
and
= 26.67
So, Jude will save = 40 + 26.67 = 66.67
But Jude saves 60
So,
Option A is incorrect.
i.e. A. Each month, Jude saves two-thirds as much money as Ted saves.
Now,
We can see that,
In 3 months, Ted will have saved the money = 120
In 2 months, Jude will have saved the money = 120
So,
Option B is correct.
i.e. B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
Also,
We can see that
In 1st month, Jude saved money 20 more than Ted saved.
In 2nd month, Jude saved money 40 more than Ted saved.
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option D is correct.
i.e. D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
∴ we get
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Answer:
18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144
b. The maximum height = 400 feet
c. Attached graph
19) The rocket will reach the maximum height after 4 seconds
20) The rocket hits the ground after 9 seconds
Step-by-step explanation:
* Lets study the rule of motion for an object with constant acceleration
# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time
and a is the acceleration of gravity
# The vertical distances h in x second is h(x) - h(0), where h(0)
is the initial height of the object above the ground
∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial
velocity, a is the acceleration of gravity (32 feet/second²) and x
is the time
18)a.
∵ The value of a = -32 ft/sec² ⇒ negative because the direction
of the motion
is upward
∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16
∴ h(x) = vx - 16x² + h(0)
∴ h(x) = -16x² + vx + h(0) ⇒ proved
* Find the height of the object after x seconds from the ground
∵ h(0) = 144 and v = 128 ft/sec
∴ h(x) = -16x² + 128x + 144
b.
* At the maximum height h'(x) = 0
∵ h'(x) = -32x + 128
∴ -32x + 128 = 0 ⇒ subtract 128 from both sides
∴ -32x = -128 ⇒ ÷ -32
∴ x = 4 seconds
- The time for the maximum height = 4 seconds
- Substitute this value of x in the equation of h(x)
∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet
c. Attached graph
19)
- The object will reach the maximum height after 4 seconds
20)
- When the rocket hits the ground h(x) = 0
∵ h(x) = -16x² + 128x + 144
∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16
∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x
∵ x² - 8x - 9 = 0
∴ (x - 9)( x + 1) = 0
∴ x - 9 = 0 OR x + 1 = 0
∴ x = 9 OR x = -1
- We will rejected -1 because there is no -ve value for the time
* The time for the object to hit the ground is 9 seconds
Answer:
x = 63
y = 47
Step-by-step explanation:
Given that the number of cookies sold is x and that of cupcakes i y, we have:
x + y = 110
2x + 4y = 314
Please see the image for the detailed steps.
