The width is 6cm
And the length is two times + 3 of the width
6 X 2 + 3 = 15
Add all 4 sides for the perimeter 6+6+15+15=42
The the dimensions are a rectangle that is 6cm wide and 15cm tall

5 0

2 years ago

A jar of peanut butter contains 454 g with a standard deviation of 10.2 g. Find the probability that a jar contains more than 46

Fofino [41]

Answer:

The probability that a jar contains more than 466 g is 0.119.

Step-by-step explanation:

We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.

Let X = <u><em>Amount of peanut butter in a jar</em></u>

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 454 g

$\sigma$ = standard deviation = 10.2 g

So, X ~ Normal( $\mu=454 , \sigma^{2} = 10.2^{2}$ )

Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)

P(X > 466 g) = P( $\frac{X-\mu}{\sigma}$ > $\frac{466-454}{10.2}$ ) = P(Z > 1.18) = 1 - P(Z $\leq$ 1.18)

= 1 - 0.881 = <u>0.119</u>

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

4 0

2 years ago

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulati

horrorfan [7]

The answer is x≥0 y≥0 x+y≤6 2x+3y≤15

5 0

2 years ago

How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ

sattari [20]

<h3>Explanation:</h3>

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

(1 -sin^2(θ))cot^2(θ) = . . . . . replace cos^2 with 1-sin^2

cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

8 0

2 years ago