Anna is going to play guitar in her school's annual concert. If she starts by practicing for one hour per day and increases the time by 30 minutes each day, how long will she practice on the seventh day? a. 140 minutes b. 210 minutes c. 240 minutes D. 300 minutes

Answers

Answer 1

Answer:

As per arithmetic progression, Anna will practice on the seventh day for 240 minutes.

What is an arithmetic progression?

"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."

Anna practices on the first day for 1 hour

$= 60$ minutes

She increases the time by 30 minutes each day.

Therefore, on the 7th day she will practice for

$= [60+(7-1)30]$ minutes

$= 240$ minutes

Learn more about an arithmetic progression here: brainly.com/question/24873057

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Answer 2

Answer: on day one she starts of with 1 hour so it will be 1+30x. X being the number of days so by the seventh day Anna would practice for 240 minutes.

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For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.

Answer:

D. $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)$

Step-by-step explanation:

Properties of normal distribution-

The normal curve is symmetrical about the mean (μ).
The mean is at the middle of the graph and it divides the area into two equal halves.
The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,

area below $-a$ , i.e $z\le -a$ ,
area between $-a$ to $a$ , i.e $-a\le z\le a$
area above $a$ , i.e $z\ge a$

Therefore, $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)=1$

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10

(-8/2)^2 = 16

What is the function written in vertex form?
A.f(x) = 3(x + 4)2 – 6
B.f(x) = 3(x + 4)2 – 38
C.f(x) = 3(x – 4)2 – 6
D.f(x) = 3(x – 4)2 – 38

Answers

Following the steps already shown to transform the given function into the vertex form, we have:

f(x) = 3(x2 - 8x + 16) + 10 - 3(16)
f(x) = 3(x - 4)(x - 4) + 10 - 48
f(x) = 3(x - 4)2 - 38

Therefore, the function written in vertex form is:
D.f(x) = 3(x – 4)2 – 38

The vertex form has the general form of:

y = a(x-h)^2 + k

We have the given equation:

f(x) = 3x^2 – 24x + 10

f(x) - 10 + 3(16) = 3(x^2 -8x + 16)
f(x) + 38 = 3(x - 4)^2
f(x) = 3 (x-4)^2 -38

Then, the correct answer is D.

Evaluate x²-6x when x=3-i.