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2 years ago

13

.If you earn $8 per hour after taxes are taken out of your paycheck and your insurance is $200 a month, how many hours will you

have to work to pay for insurance?

1 answer:

Anastaziya [24]2 years ago

4 0

200÷8= 25

25 hours would have to be worked to pay for insurance.

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Eleven percent of the pens made by Apex are defective.

sergiy2304 [10]

Let A be the event 'made by Apex and defective':
P(A) = 0.67 x 0.11 = 0.0737
Let B be the event 'made by B-ink and defective':
P(B) = 0.33 x 0.06 = 0.0198
Let C be the event 'made by Apex or B-ink and defective':
P(C) = P(A) + P(B) = 0.0737 + 0.0198 = 0.0935
P(defective and made by Apex) = 0.0737/0.0935 = 0.788
The answer is 0.788 or 78.8%.

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3 years ago

Write two numbers that multiply to the value on top and add to the<br> value on bottom.

Airida [17]

I think the answer is 2 and -15. Because 2 times - 15 is -30 and 2 and -15 can be added to -1.

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3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

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2 years ago

3. A wall is 12 feet high. If its area is 132 sq ft, what is its

dalvyx [7]

B. 46 feet because 132/12=11 and 12+12+11+11=46

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2 years ago

If one side of a square 2x-1 in, what is the perimeter in terms of x

Vesnalui [34]

(2x-1)×4=8x-4
I hope it helps ;)

5 0

3 years ago