Answer:
9:4 4:13
Step-by-step explanation:
Answer:
a) 9:4 b) 13 : 9
Step-by-step explanation:
13 = total
4 = green
13-4 ( which Is 9) = red
Ratio of red apples to green apples?
9:4
RATIO of all apples to red
13: 9
6 4 6 8 7 7 6 3 3 8 10 4 8
7 8 7 5 9 5 8 4 3 8 5 5 4
4 4 8 4 5 6 2 5 9 9 8 4 8
9 9 5 9 7 8 3 10 8 9 6
Develop a 95% confidence interval estimate of the population mean rating for Miami. If required, round your answers to two decimal places. Do not round intermediate calculations.
Answer:
The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
The sample selected is of size, n = 50.
The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:
*Use a t-table.
Compute the sample mean and sample standard deviation as follows:
Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:
Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).
Answer:
TUW=VUW
Step-by-step explanation:
Answer:
Option 3: Angle TUV = angle VUW
Step-by-step explanation:
Answer:
(a)
(b)
r'(5)= (10,75)
(c)
Step-by-step explanation:
(a)
Give that,the position vector is
r(t) = (cos 4t, sin 4t)
Differentiating with respect to t
r'(t) = (-4sin 4t, 4 cos 4t) [ and
]
To find the , we put
=(0, -4)
(b)
Give that,the position vector is
r(t) = (t²,t³)
Differentiating with respect to t
r'(t) = (2t, 3t²)
To find r'(5) , we put t=5
r'(5) = (2.5,3.5²)
= (10,75)
(c)
Given position vector is
Differentiating with respect to t
To find r'(-5) , we put t= - 5 in the above equation
For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt are:
To compute the velocity vector, we need to find the derivative of the position vector with respect to time (t). This will give us the tangent velocity vector.
A) Let r(t) = (cos4t, sin4t).
To find r'(t), we take the derivative of each component with respect to t:
r'(t) = (d/dt (cos4t), d/dt (sin4t))
r'(t) = (-4sin4t, 4cos4t)
To find r'(π/4), we substitute t = π/4 into r'(t):
r'(π/4) = (-4sin(4(π/4)), 4cos(4(π/4)))
r'(π/4) = (-4sinπ, 4cosπ)
r'(π/4) = (0, -4)
B)
To find r'(t), we take the derivative of each component with respect to t:
To find r'(5), we substitute t = 5 into r'(t):
C) Let
To find r'(t), we take the derivative of each component with respect to t:
To find r'(-5), we substitute t = -5 into r'(t):
So, the answers are:
To know more about vectors:
#SPJ3
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (p(x) ∧ r(x))
Clearly label the inference rules used at every step of your proof.
2. Consider the following hypotheses:
H1 : ∀x (¬C(x) → ¬A(x)) H2 : ∀x (A(x) → ∀y B(y)) H3 : ∃x A(x)
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (B(x) ∧ C(x))
Clearly label the inference rules used at every step of your proof.
3. Consider the following predicate quantified formula:
∃x ∀y (P (x, y) ↔ ¬P (y, y))
Prove the unsatisfiability of this formula using rules of inference.
Answer:
See deductions below
Step-by-step explanation:
1)
a) p(y)∧q(y) for some y (Existencial instantiation to H1)
b) q(y) for some y (Simplification of a))
c) q(y) → r(y) for all y (Universal instatiation to H2)
d) r(y) for some y (Modus Ponens using b and c)
e) p(y) for some y (Simplification of a)
f) p(y)∧r(y) for some y (Conjunction of d) and e))
g) ∃x (p(x) ∧ r(x)) (Existencial generalization of f)
2)
a) ¬C(x) → ¬A(x) for all x (Universal instatiation of H1)
b) A(x) for some x (Existencial instatiation of H3)
c) ¬(¬C(x)) for some x (Modus Tollens using a and b)
d) C(x) for some x (Double negation of c)
e) A(x) → ∀y B(y) for all x (Universal instantiation of H2)
f) ∀y B(y) (Modus ponens using b and e)
g) B(y) for all y (Universal instantiation of f)
h) B(x)∧C(x) for some x (Conjunction of g and d, selecting y=x on g)
i) ∃x (B(x) ∧ C(x)) (Existencial generalization of h)
3) We will prove that this formula leads to a contradiction.
a) ∀y (P (x, y) ↔ ¬P (y, y)) for some x (Existencial instatiation of hypothesis)
b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)
c) P (x, x) ↔ ¬P (x, x) (Take y=x in b)
But c) is a contradiction (for example, using truth tables). Hence the formula is not satisfiable.
Answer: Set up the ratio as a fraction and divide by the gallons. 90/5 = 18/1 The ratio is 18 miles/gallon.