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3 years ago

Find the pay earned? of 33 hours at $5.15 per hour

Mathematics

1 answer:

Alecsey [184]3 years ago

8 0

33 * 5.15 = 169.95. 33 hours at 5.15 per hour

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Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

<u>Step-by-step explanation:</u>

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

$\bullet\quad a=\dfrac{1}{4p}$

p is the distance from the vertex to the focus

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

***************************************************************************************

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

3 years ago

Can someone help me answer these questions

Vlad1618 [11]

We can't see the questions from this picture of you show a picture that we can see or type the answers we can answer

4 0

3 years ago

The Tampa Times polled 1,457 adults in the city to determine whether they put on their shirt before they put on their pants. Of

Morgarella [4.7K]

Answer:

The mean is 0.32 and the standard deviation is 0.0122.

Step-by-step explanation:

Given that the Tampa Times polled 1,457 adults in the city to determine whether they put on their shirt before they put on their pants.

Of the respondents, 48% said they put their shirt on first.

32% of all adults actually put their shirt on first

i.e. sample proportion is 48% while population proportion is 32%

Hence sampling distribution follows a distribution with mean = population proportion p

Hence here mean = 0.32

Std deviation of sampling distribution = $\sqrt{\frac{pq}{n} } =\sqrt{\frac{0.32(0.68)}{1457} } \\=0.0122$

Hence option 3) The mean is 0.32 and the standard deviation is 0.0122.

is right

3 0

3 years ago

Picturing the way a volcano erupts to remember how a volcano functions is called

SOVA2 [1]

The correct answer to this question is letter A which is visualizing. Visualizing is the act of picturing a certain situation in your head to recall how it works. In this example, you want to remember how a volcano functions. A volcano erupts. So in order to remember this, you picture in your mind a volcano that is erupting. So once you are asked a question about the functions of a volcano, your mind will immediately show the picture of a volcano erupting.

8 0

3 years ago

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Emma works at a restaurant that shares any money earned from tips evenly amongst the staff. On a particular night, Emma was paid

steposvetlana [31]

Answer:

$89.15

Step-by-step explanation:

50/4= 12.50

12.50+76.65= 89.15

4 0

3 years ago