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Pachacha [2.7K]

2 years ago

14

An empty tank is filled with water at a constant rate. The table shows w, the number of gallons of water in the tank after m min

utes.
Table:
8 : 132
18 : 297
26 : 429

1 answer:

Tpy6a [65]2 years ago

3 0

Dnbagtshhejxgg no Gus

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The two intervals (114.9, 115.7) and (114.6, 116.0) are confidence intervals (computed using the same sample data) for μ = true

kenny6666 [7]

Answer:

115.3 hertz

Step-by-step explanation:

For either interval, the value of the sample mean is given by the average of the lower and upper bound of the confidence interval. Since both intervals were constructed by using the same sample, both values should be equal.

For the first interval:

$M=\frac{114.9 + 115.7}{2} \\M=115.3\ hertz$

For the second interval:

$M=\frac{114.6 + 116.0}{2} \\M=115.3\ hertz$

4 0

3 years ago

The expression n2 + n represents the total number of blocks used in the nth figure of a pattern. Use the equation n2 + n = 56 to

Brrunno [24]

We have to solve this quadratic equation $n^{2}+n=56$ for n to get <em>which figure has 56 blocks</em>.

$n^{2}+n=56\\n^{2}+n-56=0$

For middle term factorization, we need <em>two numbers that multiplied gives us -56 and added gives us 1 (coefficient of n).</em>

<em>Such two numbers are </em><em>8</em><em> and </em><em>-7</em><em>. We can now write,</em>

<em> $n^{2}+n-56=0\\(n+8)(n-7)=0\\n=-8, 7$ </em>

<u><em>"There is no negative figure number possible, so we disregard -8"</em></u>

Our answer is 7.

ANSWER: The 7th figure has 56 blocks.

3 0

3 years ago

Read 2 more answers

In oak valley the cost of gas averaged $3.50 per gallon qt the start of April the rose 6% during April and dropped 10% during Ma

andreev551 [17]

Answer:

$ 3.34

Step-by-step explanation:

3.50 * 1.06 cost at end of April then find 90% of this to find end of May

3.50 * 1.06 * .9 = $ 3.34

8 0

2 years ago

What is 884 divided by 3

matrenka [14]

Answer:

294.6666666666667

3 0

2 years ago

Read 2 more answers

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

harina [27]

$L(x,y,z,\lambda)=8x+8y+4z+\lambda(4x^2+4y^2+4z^2-36)$

$L_x=8+8\lambda x=0\implies 1+\lambda x=0$
$L_y=8+8\lambda y=0\implies 1+\lambda y=0$
$L_z=4+8\lambda z=0\implies 1+2\lambda z=0$
$L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9$

$yL_x=y+\lambda xy=0$
$xL_y=x+\lambda xy=0$
$\implies yL_x-xL_y=y-x=0\implies y=x$

$2zL_x=2z+2\lambda xz=0$
$xL_z=x+2\lambda xz=0$
$\implies 2zL_x-xL_z=2z-x=0\implies x=2z$

$2zL_y=2z+2\lambda yz=0$
$yL_z=y+2\lambda yz=0$
$\implies 2zL_y-yL_z=2z-y=0\implies y=2z$

$x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1$

$z=\pm1\implies y=x=\pm2$

So we have two critical points, (2, 2, 1) and (-2, -2, -1), which respectively give a max of 36 and a min of -36.

5 0

3 years ago