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3 years ago

Population mean = 80

Mathematics

1 answer:

alexira [117]3 years ago

4 0

Answer:

The answer is : 0.0597

Step-by-step explanation:

Population mean = μ = 80

Standard deviation = σ = 20

Sample = N = 60

σ_mean = σ/√N

= (20)/√(60) = 2.582

Now we will find z1 and z2.

z1 = {(84) - μ}/σ_mean = ${(84)-(80)}/(2.582)= 1.549$

z2 = {(88) - μ}/σ_mean = ${(88)-(80)}/(2.582)= 3.098$

Now probability that the sample mean will be between 84 and 88 is given by:

Prob{ (1.549) ≤ Z≤ (3.098) } = (0.9990) -(0.9393) = 0.0597

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What is the discriminant of the polynomial below? 2x^2+3x-7

Katena32 [7]

Answer:

Option C. $65$

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$D=b^{2}-4ac$

in this problem we have

$2x^{2} +3x-7$

$a=2\\b=3\\c=-7$

substitute

$D=3^{2}-4(2)*(-7)$

$D=9+56$

$D=65$

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3 years ago

How many diagonals does the regular polygon have

VLD [36.1K]

Answer:3

Step-by-step explanation:

6 0

3 years ago

Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60 % of his collection.How many toy cars do

Kryger [21]

60% of what equals 27? This is the question. "Of" always means multiply.

So... convert the percent to a decimal: .6x=27.

Divide: x=27/.6
x=45

Plug it back in to check: .6(45)=27
27=27.

Or: 27/45=.6
.6=.6

8 0

3 years ago

Read 2 more answers

A Rectangle with sides 100m and 50m. Person B and Person A start walking in the opposite direction at the same point with veloci

Maurinko [17]

Answer:

It takes takes them 31.67 secs to meet after Person A starts walking

34.67 secs after Person B starts walking

Step-by-step explanation:

First, we will find the perimeter of the rectangle

From,

Perimeter of rectangle = 2 ( $l$ + $b$ )

Where $l$ is the length

and $b$ is the breadth

From the question, $l$ = 100m

and $b$ = 50m

Hence,

Perimeter of the rectangle = 2 (100+50)

= 2(150) = 300m

Hence, the perimeter of the rectangle is 300m

This is the total distance that will be covered by both persons by the time they meet.

Let the distance covered by person A be $S_{1}$

and the distance covered by person B be $S_{2}$

We can write that

$S_{1}$ + $S_{2}$ = 300m

Velocity of person A, $V_{A}$ = 4 m/s

and velocity of person B, $V_{B}$ = 5 m/s

From the question, Person A starts walking 3 seconds after person B,

This means, if person A spends $t$ secs before they meet, then person B would spend (3 + $t$ ) secs.

For Person A,

Velocity = 4 m/s

Time = $t$ secs

Distance = $S_{1}$

From,

$Velocity = \frac{Distance}{Time}$

Then,

$Distance = Velocity \times time$

$S_{1} = 4 \times t$

$S_{1} = 4t$ ...... (1)

For Person B

Velocity = 5 m/s

Time = (t + 3) secs

Distance = $S_{2}$

Also, from

$Distance = Velocity \times time$

$S_{2} = 5 \times (3+t)$

$S_{2} = 5(3+t)$ ...... (2)

Recall that, $S_{1}$ + $S_{2}$ = 300m

Then, $S_{2}$ = 300m - $S_{1}$

We can then write that,

300m - $S_{1}$ $= 5(3+t)$

Then,

$S_{1} = 300 - 5(3+t)$ ..... (3)

Equating equations (1) and (3), we get

$300 - 5(3+t) = 4t$

$300 - 15 -5t = 4t\\9t = 285\\t = \frac{285}{9}\\$

$t = 31.67 secs$

This is the time spent by Person A

Hence, it takes takes them 31.67 secs to meet after Person A starts walking OR

34.67 secs after Person B starts walking

3 0

3 years ago

Write an explicit formula for An, the nth term of the sequence 7, -42, 252, ....

erik [133]

Answer:

$A_n = 7(-6)^{n-1}$

Step-by-step explanation:

Key skills needed: Explicit formula, Geometric sequence

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7 or 252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

--> r means the constant (or common ratio) that is being multiplied.

--> $a_1$ means the first term

--> $a_n$ means the "nth" numbered term (so $a_3$ is the 3rd term, $a_{10}$ is the 10th term and so on).

--> $n-1$ is just the "n" in $a_n$ minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> $r = -6$ (Since we got -6 as the constant/common ratio).

--> $a_1 = 7$ (Since 7 is the 1st term)

This means that our formula would be --> $A_n = 7(-6)^{n-1}$

Hope you understood and have a nice day!! :D

8 0

3 years ago