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2 years ago

7

The price of orange juice is believed to increase by 14% over the next year. If a gallon of orange juice costs $3.00 now, what w

ill the price be in a year, after the increase?
$

1 answer:

Sergio039 [100]2 years ago

7 0

$3.42

Take the original price and multiply by 1.14

Explanation: 1.14 comes from the whole (1) of the orange juice at the time plus the percent (14% ---> .14).

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Can anybody show me how to do this half angle identity problem STEP BY STEP? I always seem to be missing something

klio [65]

Answer: $\bold{-\dfrac{7\sqrt2}{10}}$

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

It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ $cos\ \dfrac{\theta}{2}$

It is given that sin θ = $-\dfrac{7}{25}$ ⇒ y = -7 & hyp = 25

Use Pythagorean Theorem to find "x":

x² + y² = hyp²

x² + (-7)² = 25²

x² + 49 = 625

x² = 576

x = 24

Use the "x" and "hyp" values to find cos θ:

$cos\ \theta=\dfrac{x}{hyp}=\dfrac{24}{25}$

Lastly, input cos θ into the half angle formula:

$cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}$

Reminder: We previously determined that the half-angle will be negative.

6 0

2 years ago

Find x.<br> X=<br> 400<br> 8<br> Round to two decimals at each step of the problem.

svlad2 [7]

Answer:

6.71

Step-by-step explanation:

→ Find a triangle to use

Tan = Opposite ÷ Adjacent

→ Rearrange to make opposite the subject

Opposite = Tan × Adjacent

→ Substitute in the values

Opposite = Tan (40) × 8

→ Simplify

Opposite = 6.71

4 0

3 years ago

What is a number that is greater than 5 and less than 40, is not divisible by 2, the sum of it's digits is 7 and has exactly 3 f

Doss [256]

Is odd between 5 and 40 is a square number and the digits add to 7.
all the square numbers between there are 9,16, 25, 36
It's not 9, 16 or 36 so it has to be 25

Hope this helps :)

4 0

3 years ago

At the grocery store, Mr. and Mrs. Bailey bought 24 apples and 18 pears. Write a ratio in simplest form to compare apples and pe

Oliga [24]

Answer:

4:3

Step-by-step explanation:

Legit just simplified it.The original ratio is 24:18. First found the greatest common multiple (GCF) and divided both by it. In this case it was 6. So 24/6 = 4 and 18/6 = 3. Now your newly simplified ratio of apples to pears is 4:3.

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2 years ago

A circle is inscribed in a square, as shown in the figure below. The length of

mafiozo [28]

Answer:

78.5 cm^2

Step-by-step explanation:

the circle's diameter is 10cm --> its radius is 5cm

the area of the circle is 5^2 x 3.14 = 78.5cm^2

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3 years ago