1. Consumers who bought Silly Soup were naked to respond to an internet wurvey comparing,

How can csc^2-cot^2 = 1?

Softa [21]

ANSWER

By simplifying the left hand side using the Pythagorean Identity.

EXPLANATION

The given identity is

$\csc^{2} (x) - \cot^{2} (x) = 1$

Take the left hand side and simplify to get the right hand side.

$\csc^{2} (x) - \cot^{2} (x) = \frac{1}{\sin^{2} (x)} - \frac{ \cos^{2} (x)}{\sin^{2} (x)}$

Collect LCM for the denominators.

$\csc^{2} (x) - \cot^{2} (x) = \frac{1 - \cos^{2} (x)}{\sin^{2} (x)}$

Recall the Pythagorean Identity.

$\cos^{2} (x) + \sin^{2} (x) = 1$

This implies that:

$1 - \cos^{2} (x) = \sin^{2} (x)$

We substitute this to get,

$\csc^{2} (x) - \cot^{2} (x) = \frac{\sin^{2} (x)}{\sin^{2} (x)}$

$\csc^{2} (x) - \cot^{2} (x) = 1$

6 0

2 years ago

Please. please. please. help

Elza [17]

Answer:

kjh7563653 365385 36539y5 53nkddg dhdk djgd ghgkg d99 76 79

Step-by-step explanation:

5 0

2 years ago

Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.

alisha [4.7K]

Answer:

(a) 1, 2, 3, 6, 8

Step-by-step explanation:

Given

$Median = 3$

$Mean = 4$

Required

The sequence of hours worked each day

<em>See attachment for options</em>

From the question, we understand that:

$Median = 3$

This means that, the middle number is 3 (when sorted)

So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively

Next, is to determine the mean of (a) and (d)

The mean of a data is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

(a)

$\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}$

$\bar x = \frac{20}{5}$

$\bar x = 4$

(d)

$\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}$

$\bar x = \frac{15}{5}$

$\bar x = 3$

Option (a) is true, because it has:

$Median = 3$

$Mean = 4$

7 0

2 years ago

A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift,

Snezhnost [94]

Answer:

0.2941 = 29.41% probability that it was manufactured during the first shift.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured during the first shift.

Probability of a defective item:

1% of 50%(first shift)

2% of 30%(second shift)

3% of 20%(third shift).

So

$P(A) = 0.01*0.5 + 0.02*0.3 + 0.03*0.2 = 0.017$

Probability of a defective item being produced on the first shift:

1% of 50%. So

$P(A \cap B) = 0.01*0.5 = 0.005$

What is the probability that it was manufactured during the first shift?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941$

0.2941 = 29.41% probability that it was manufactured during the first shift.

6 0

2 years ago

Over 6.8 months, a tree grew 7.48 inches.

evablogger [386]

The tree's grow rate is 1.1 per month
7.48/6.8
=1.1

4 0

3 years ago

Read 2 more answers