A 35-foot ladder leans against a building so that cos B = 0.3.

PLEASE HELP!

Leona [35]

Answer:

The initial temperature of the object was 37.6

Step-by-step explanation:

we have

$f(t)=Ce^{(-kt)} +20$

where

f(t) represent the temperature of the object in degree Celsius

t is the time in minutes

Find the value of the constant C

we have the ordered pair (4,35)

substitute in the equation and solve for C

$35=Ce^{(-0.0399*4)} +20\\Ce^{(-0.0399*4)}=15\\C=15/e^{(-0.0399*4)}\\C=17.6$

Find the initial value of the object

we know that

The initial temperature is the value of f(t) when the value of t is equal to zero

so

For t=0

$f(0)=(17.6)e^{(-k*0)} +20\\f(0)=17.6 +20\\f(0)=37.6$

therefore

The initial temperature of the object was 37.6 (I not include units)

7 0

3 years ago

If two expressions, 2x + 8 and 2 (x + 2) + k are equivalent, what is the value of k? Enter the value in the box.

Nitella [24]

2x+8=2(x+2)+k
2x+8=2x+4+k
k=4

Therefore k= 4, Hope this helps!! :)

5 0

3 years ago

What is the whole number of 729? Please helppp

Vlada [557]

Answer:

729

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

She would like to buy the sheet that meets here requirements for high quality and has the lowest price per square meter. Which o

goblinko [34]

What kind of sheet is the sheet that she wants to buy?

6 0

4 years ago

In a survey of US adults, twenty percent say they never exercise. This is the highest level seen in five years.

Andrews [41]

Answer:

$0.20 - 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.175$

$0.20 + 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.225$

The 95% confidence interval would be given by (0.175;0.225)

Step-by-step explanation:

Assuming this question: In a survey of 1000 US adults, twenty percent say they never exercise. This is the highest level seen in five years.1 Find a 95% confidence interval for the proportion of US adults who say they never exercise. Round your answers to three decimal places.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.20 - 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.175$

$0.20 + 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.225$

The 95% confidence interval would be given by (0.175;0.225)

6 0

3 years ago