Find f. f'(x)=(sqrt(x))(6+10x) f(1)=11

a boat traveled 160 miles downstream and back. the trip downstream took 8 hours. the trip back took 40 hours. find the speed of

Nana76 [90]

Let speed of the boat in still water = x miles per hour

Let speed of the current = y miles per hour

When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)

now plug the given values in formula speed=distance/time

we get equation:

(x+y)=160/8

or x+y=20...(i)

When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)

now plug the given values in formula speed=distance/time

we get equation:

(x-y)=160/40

or x-y=4

or x=4+y...(ii)

plug value of x into (i)

4+y+y=20

4+2y=20

2y=16

y=8

plug value of y into (ii)

x=4+8=12

Hence final answer is given by:

Speed of the boat in still water = 12 miles per hour

Speed of the current = 8 miles per hour

4 0

3 years ago

A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jace

Leni [432]

Answer:

44.4

Step-by-step explanation:

yes

5 0

3 years ago

15/9 =25/9x I simplified it as much as I could but i'm stuck here:/

kvv77 [185]

Answer:

Step-by-step explanation:

We move all terms to the left: 15/9-(25/9x)=0 Domain of the equation: 9x)!=0 x!=0/1 x!=0 x∈R

We add all the numbers together, and all the variables

-(+25/9x)+15/9=0

We get rid of parentheses

-25/9x+15/9=0

We calculate fractions

=0 x=0/1 x=0

i hope helps you and if you want you can give me a brainly crown only if you want

4 0

3 years ago

Read 2 more answers

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

Part b

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

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

Solve for x. 4x +4=12

PolarNik [594]

Answer:

x = 2

Step-by-step explanation:

4x +4=12

-4. -4

4x.= 8

divide both saide by 4

x. = 2

8 0

3 years ago