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Which equation is equivalent to x + 8 = 21?

soldi70 [24.7K]

Answer:

b

13+8=21

21×4=84

84÷4=21

3 0

2 years ago

Evaluate lim θ→0 sin(cos 8θ)/sec 5θ.

kenny6666 [7]

In this case, we are given with the expression <span>sin(cos 8θ)/sec 5θ and is asked to evaluate the expression with limit as theta approaches 0. In this case, we just substitute 0 to theta. cos 0 is equal to 1 hence sec 0 is also equal to 1. sin theta is equal to 0.0175. Answer os 0.0175.</span>

8 0

2 years ago

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A triangle has 34 degree angle and a 102 degree angle what is the third angle

coldgirl [10]

Answer: 44 degrees.

Step-by-step explanation: Since the sum of the measures of the angles in a triangle add up to 180 degrees, we can figure out the measure of the third angle by adding the first two angles and subtracting the sum from 180. 102 + 34 = 136. 180 - 136 = 44, so the measure of the third angle is 44 degrees.

8 0

2 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

In 2009, the American Time Use Survey found that the average American spends 2.8 hours a day watching TV. Suppose the standard d

Anit [1.1K]

Answer:

4.72 hours/day

Step-by-step explanation:

Mean time spent watching TV (μ) = 2.8 hours a day

Standard deviation (σ) = 1.5 hours a day

The 90th percentile (upper 10%) of a normal distribution has an equivalent z-score of roughly z = 1.282. The minimum time spent watching TV, X, at the 90th percentile is:

$z=\frac{X-\mu}{\sigma} \\1.282=\frac{X-2.8}{1.5}\\ X=4.72\ hours/day$

On a typical day, you must watch at least 4.72 hours of TV to be in the upper 10%.

8 0

3 years ago