Complete the following statement (12 pts.) 5 - (__) = 14 __

Find the difference. (3 • 1,000) – (2 • 100)

hodyreva [135]

Answer:

3x1000=3000

2x100=200

3000-200=2800

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Approximate the change in the volume of a sphere when its radius changes from r = 30 ft to r=10.1 ft [v(r)=4/3Ï€r^3]. When r cha

ella [17]

Answer: ∆V for r = 10.1 to 10ft

∆V = 40πft^3 = 125.7ft^3

Approximate the change in the volume of a sphere When r changes from 10 ft to 10.1 ft, Î”V=_________

[v(r)=4/3Ï€r^3].

Step-by-step explanation:

Volume of a sphere is given by;

V = 4/3πr^3

Where r is the radius.

Change in Volume with respect to change in radius of a sphere is given by;

dV/dr = 4πr^2

V'(r) = 4πr^2

V'(10) = 400π

V'(10.1) - V'(10) ~= 0.1(400π) = 40π

Therefore change in Volume from r = 10 to 10.1 is

= 40πft^3

Of by direct substitution

∆V = 4/3π(R^3 - r^3)

Where R = 10.1ft and r = 10ft

∆V = 4/3π(10.1^3 - 10^3)

∆V = 40.4π ~= 40πft^3

And for R = 30ft to r = 10.1ft

∆V = 4/3π(30^3 - 10.1^3)

∆V = 34626.3πft^3

3 0

4 years ago

An article in Fire Technology describes the investigation of two different foam expanding agents that can be used in the nozzles

kvv77 [185]

Answer:

a) There is no evidence to support the claim that there is no difference in mean foam expansion of these two agents.

b) P=0

c) 90% CI

$-3.2406\leq \mu_1-\mu_2 \leq -2.2614$

This CI tells us that there is a 90% confidence that the real value of the difference between the means is between this two values. We see that both are negative values, so the value 0 is left out of the interval.

That means we can be almost sure both means don't have the same value, confirming the results of the previous test.

Step-by-step explanation:

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a: \mu_1-\mu_2\neq 0$

The significance level is 0.10 and it will be a two-tailed test.

The difference of the sample means is:

$M_d=M_1-M_2=4.340-7.091=-2.751$

As the sample size is equal for both samples, the estimated standard error of the difference between means is calculated as:

$s_M_d=\sqrt{\frac{s_1^2+s_2^2}{N}}= \sqrt{\frac{0.508^2+0.430^2}{5}}=\sqrt{\frac{0.442964}{5} }= \sqrt{0.0886}=0.2976$

Then, the statistic z is:

$z=\frac{M_d-(\mu_1-\mu_2)}{s_M_d}=\frac{-2.751-0}{0.2976}=-9.24\\\\P(|z|>9.24)=0$

The P-value (P=0) is much lower than the significance level, so the null hypothesis is rejected. The means are different.

For a 90% confidence interval for the difference of the means, we use a z=1.645.

Then the confidence interval is defined as:

$M_d-z*s_M_d\leq \mu_1-\mu_2 \leq M_d-z*s_M_d\\\\-2.751-1.645*0.2976\leq \mu_1-\mu_2 \leq -2.751+1.645*0.2976\\\\-3.2406\leq \mu_1-\mu_2 \leq -2.2614$

This CI tells us that there is a 90% confidence that the real value of the difference between the means is between this two values. We see that both are negative values, so the value 0 is left out of the interval.

That means we can be almost sure both means don't have the same value.

5 0

3 years ago

Please Help Quickly!!! Find the limit if f(x) = x^3

jeka94

Answer:

Option b. 12

Step-by-step explanation:

This exercise asks us to find the derivative of a function using the definition of a derivative.

Our function is $f(x) = x^{3}$ . Therefore: