PLEASE HELP!!!!!!!!Rewrite the following compound statement as a biconditional.

If it rains, then I use an umbrella, and if I use an umbrella, then it is raining.

a. If I use an umbrella, then it is raining.
b. If my umbrella is broken, then it is not raining.
c. I use an umbrella, if it rains.
d. I use an umbrella if and only if it rains.

Answers

Answer 1

Answer: I think the correct answer from the choices listed above is option D. A biconditional statement is defined to be true whenever both parts have the same truth value. Therefore, the statement would be "I use an umbrella if and only if it rains." Hope this answers the question. Have a nice day.

Answer 2

Answer:

Answer:

Your answer would be D.

I use an umbrella if and only if it rains.

Trust me on this it makes a lot of since

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Simplify (-2)(-3)^2 -2(2 - 5)

Answers

When solving this problem, PEMDAS is a key component. What is PEMDAS?
PEMDAS stands for the following:
P- Parentheses
E- Exponents
M-Multiplication
D- Division
A-Addition
S-Subtraction
This is also known as order of operations. Following this order, we can easily simplify the problem.

P-Parentheses
(-2)(-3)^2-2(2-5)
Our parentheses is (2-5). We can simply this to -3. Our problem now is
(-2)(-3)^2-2(-3)

E-Exponents
We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is
(-2)(9)-2(-3)

M- Multiplication
We can simply to.
-18+6

These simplifies into
-12

Final answer:

To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.

Explanation:

To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:

First, we calculate (-3)^2, which is equal to 9.
Next, we substitute the values in the expression: (-2)(9) - 2(2 - 5).
Then, we simplify the expression inside the parentheses: (-2)(9) - 2(-3).
Multiplying -2 by 9 gives us -18, and multiplying 2 by -3 gives us -6.
Finally, we subtract -6 from -18 to get the final result, which is -12.

Therefore, the simplified expression is -12.

Learn more about Simplifying expressions here:

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For a spinning amusement park ride, the velocity v in meters per second of a car moving around a curve with a radius r meters is given by the formula v=sqrt(ar), where 'a' is the car’s acceleration in m/s^2.a) For safety reasons, a ride has a minimum acceleration of 39.2m/s^2 . If the cars on the ride have a velocity of 14m/s what is the smallest radius that any curve on the ride may have?

b) What is the acceleration of a car moving at 8m/s around a curve with a radius of 2.5m?

Answers

The smallest radius will be, r = 5 m. And the acceleration of a car is, a = 25.6 m/s².

What is acceleration?

Acceleration is the ratio of the change of the velocity with respect to time or the rate of change of the velocity.

a.The relation between the velocity, the radius of the path, and the acceleration on the circular path is given by :

Acceleration, a = 39.2 m/s²

Velocity of the car, v = 14 m/s

The radius of the path can be calculated using the above formula i.e.

$r=(v^2)/(a)$

$r=((14)^2)/(39.2)$

r = 5 m

b. Velocity of the car, v = 8 m/s

The radius of the path, r = 2.5 m

The acceleration of the car is given by :

$a=(8^2)/(2.5)$

a = 25.6 square meter.

Therefore, the smallest radius will be, r = 5 m. And the acceleration of a car is, a = 25.6 m/s².

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a)
v=sqrt(ar)
v^2=ar
r=(v^2)/a
r=(14^2)/39.2
r=5

5 m

b)
v=sqrt(ar)
v^2=ar
a=(v^2)/r
a=(8^2)/2.5
a=25.6

25.6ms^-2

Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown.(a) Find P '(2). (b) Find Q'(7).

Answers

Hello,

Very nice like question!

a)
F(2)=3 ; G(2)=2
F'(2)=0; G'(2)=1/2
P'(x)=F'(x)*G(x)+F(x)*G'(x)

P'(2)=0*2+3*1/2=3/2

b)
F(7)=5; G(7)=1
F'(7)=1/4; G'(7)=-2/3

Q'(x)=(F'(x)*G(x)-F(x)*G'(x)) / G²(x)

Q'(7)=(1/4*1-5*(-2/3))/1²=1/4+5/3=23/12

Celeste wants to have her hair cut and permed and also go to lunch. She knows she will need $95. The perm costs twice as much as her haircut and she needs $5 for lunch. How much does the perm cost?

Answers

so perm cost 2 times as hair cut
perm=2 times haircut
she also needs 5 dollars for lunch

so therefor if 95 is enough to cover it we do
cost=lunch+perm+haircut
cost=5+perm+haircut
subsitute
95=5+2 times haircut+1 time haircut
add like terms
95=5 +3 times haircut
subtract 5 from both sides
90=3 times haircut
diide by 3
30=haircut
subsitute
perm=2 times haircut=2 times 30=60

perm=$60

A line is a(n) _____ for a function if the graph of the function gets closer and closer to touching the line but never reaches it. A. asymptote B. diagonal C. array D. diagram E. estimation

Answers

I think the correct answer from the choices listed above is option A. A line is an asymptote for a function if the graph of the function gets closer and closer to touching the line but never reaches it. Hope this answers the question. Have a nice day.

Factor 20x2 + 25x - 12x - 15 by grouping.

Answers

Answer:

(4x + 5)(5x - 3).

step-by-step explanation:

20x^2 + 25x - 12x - 15 by grouping:

Start with the expression:

20x^2 + 25x - 12x - 15.

Group the terms in pairs, like this:

(20x^2 + 25x) - (12x + 15).

Now, look for the greatest common factor (GCF) in each group:

In the first group
(20x^2 + 25x), the GCF is 5x because both terms are divisible by 5x.

So, factor out 5x: 5x(4x + 5).

In the second group (12x + 15), the GCF is 3 because both terms are divisible by 3.

So, factor out 3: 3(4x + 5).

Now, your expression looks like this:

5x(4x + 5) - 3(4x + 5).

Notice that both groups have the common factor (4x + 5).

Factor this out: (4x + 5)(5x - 3).

So, the factored form of 20x^2 + 25x - 12x - 15 is (4x + 5)(5x - 3)

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