Yall shiuld like kinda help... youll be marked as “brainliest”

An article in Fire Technology investigated two different foam-expanding agents that can be used in the nozzles of firefighting s

UNO [17]

Answer:

Step-by-step explanation:

Hello!

The objective of this experiment is to test if two different foam-expanding agents have the same foam expansion capacity

Sample 1 (aqueous film forming foam)

n₁= 5

X[bar]₁= 4.7

S₁= 0.6

Sample 2 (alcohol-type concentrates )

n₂= 5

X[bar]₂= 6.8

S₂= 0.8

Both variables have a normal distribution and σ₁²= σ₂²= σ²= ?

The statistic to use to make the estimation and the hypothesis test is the t-statistic for independent samples.:

t= $\frac{(X[bar]_1 - X[bar]_2) - (mu_1 - mu_2)}{Sa*\sqrt{\frac{1}{n_1} + \frac{1}{n_2 } } }$

a) 95% CI

(X[bar]_1 - X[bar]_2) ± $t_{n_1 + n_2 - 2}$ * $Sa* \sqrt{\frac{1}{n_1}+\frac{1}{n_2} }$

Sa²= $\frac{(n_1-1)S_1^2 + (n_2-1)S_2^2}{n_1 + n_2 - 2}$ = $\frac{(5-1)0.36 + (5-1)0.64}{5 + 5 - 2}$ = 0.5

Sa= 0.707ç

$t_{n_1 + n_2 -2: 1 - \alpha /2} = t_{8; 0.975} = 2.306$

(4.7-6.9) ± 2.306* $(0.707\sqrt{\frac{1}{5}+\frac{1}{5} })$

[-4.78; 0.38]

With a 95% confidence level you expect that the interval [-4.78; 0.38] will contain the population mean of the expansion capacity of both agents.

b.

The hypothesis is:

H₀: μ₁ - μ₂= 0

H₁: μ₁ - μ₂≠ 0

α: 0.05

The interval contains the cero, so the decision is to reject the null hypothesis.

Complete question

a. Find a 95% confidence interval on the difference in mean foam expansion of these two agents.

b. Based on the confidence interval, is there evidence to support the claim that there is no difference in mean foam expansion of these two agents?

8 0

3 years ago

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?

stepladder [879]

Answer:

$\displaystyle 64$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Rule [Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to c} x^n = c^n$

Limit Property [Multiplied Constant]: $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{x \to 0} f(x) = 4$

Step 2: Solve

Rewrite [Limit Property - Multiplied Constant]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4$
Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)$
Simplify: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

3 0

3 years ago

PLZ HELP WILL MARK BRAINLIEST 50 POINTS REAL NUMBER SYSTEM

Leokris [45]

Answer:

B and J switch because J is a repeating number and repeating numbers are irrational because they don't have a definte end. Other than that, you are good!

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Write an expression with a negative exponent that has a value between 0 and 1/2

aliya0001 [1]

Exponent is a number used to express shorter equation; it is a number that says how many times you are going to multiply the base number.

Exponents have several laws, here are some:
=> x^1 = x
=> x^0 = 1
=> x^-1 = 1/x
=> x^m x^n = X^m+n
=> x^m/x^n = x^m-n

And since we were asked to write an expression with a negative exponent that has a value between 0 and ½
=> 2^ -2 = ½

4 0

3 years ago

Amy, Dan, and Mike are competing in a cooking competition. They all used different amounts of milk from a container holding 6 ga

zmey [24]

Answer:

Amy: 0.78 Gallons

Dan : 0.14 Gallons

Mike: 0.5 Gallons

Answer: Amy

Step-by-step explanation:

Look closely

8 0

3 years ago