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3 years ago

I can't solve question 11 please help

Mathematics

1 answer:

hammer [34]3 years ago

7 0

24 divided by 3 = 8
So if the barge takes only 2 hours during the return trip. We multiply 2 hours by 8 miles to get a total of 16 hours.

The answer is 16

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The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression.

konstantin123 [22]

The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.

The expression shown is an exponential expression. An exponential expression usually takes the form $ab^{x}$ , as this one does. A represents the initial value, in this case-the initial number of bacteria. B represents the growth rate. When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion. In this case, a=57, and b=0.31.

Hope this makes sense!

3 0

3 years ago

A researcher surveyed 150 high school students and found that 68% played a musical insturment. What would be a reasonable range

maria [59]

Answer:

The reasonable range for the population mean is (61%, 75%).

Step-by-step explanation:

The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.

The mean of the sampling distribution of sample proportion is, $\hat p$ .

One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

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

Given:

n = 150

$\hat p$ = 0.68

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for proportion as follows:

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

$=0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)$

Thus, the reasonable range for the population mean is (61%, 75%).

5 0

3 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

Highest (-3,-3)

Lowest (2,2)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

Add me on snap gamerdylan19 insta is reaper_shot and tiki's Tok is death_shot55

3241004551 [841]

Answer:

ok xd

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Решите уравнение

mafiozo [28]

Answer:

a)-6(x-2) = 4r-17

B) 10x +307 - 20) = 13-20

6) (18-19) -(4-720) = -73

г)-3(4-5y)+2(3-6y)=-39

3 0

3 years ago