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Butoxors [25]
3 years ago
11

A cafeteria manager needs to know how many apples and bananas to to order. He asked students to choose either an apple or a bana

na as their preferred fruit. The survey results know that of the students who responded, 7/10 picked apples. If 84 students picked apples, how many picked bananas?
Mathematics
1 answer:
shusha [124]3 years ago
5 0

Answer:

36

Step-by-step explanation:

The answer is easy to find if we use the cross-multiplication method.

We know 7 students out of 10 picked apples, then 3 out of 10 picked bananas.

We know the number of people who picked apples.

\frac{apples}{bananas} = \frac{7}{3} = \frac{84}{x}

We just have to isolate x, this way and solve the problem:

\frac{7}{3} = \frac{84}{x}

becomes

x = \frac{84 * 3}{7} = \frac{252}{7} = 36

So, 36 students picked bananas as their favorite fruit.

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The value pi/4 is a solution for the equation 3 sqrt 2 cos theta+2=-1
natulia [17]

Answer:

<h2>FALSE</h2>

Step-by-step explanation:

3\sqrt2\cos\theta+2=-1\\\\\text{Method 1}\\\\\text{Put}\ \theta=\dfrac{\pi}{4}\ \text{to the equation and check the equality:}\\\\\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\L_s=3\sqrt2\cos\dfrac{\pi}{4}+2=3\sqrt2\left(\dfrac{\sqrt2}{2}\right)+2=\dfrac{(3\sqrt2)(\sqrt2)}{2}+2\\\\=\dfrac{(3)(2)}{2}+2=3+2=5\\\\R_s=-1\\\\L_s\neq R_s\\\\\boxed{FALSE}

\text{Method 2}\\\\\text{Solve the equation:}\\\\3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\\\\3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\\\\\cos\theta=-\dfrac{3}{3\sqrt2}\\\\\cos\theta=-\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\\cos\theta=-\dfrac{\sqrt2}{2}\to\theta=\dfrac{3\pi}{4}+2k\pi\ \vee\ \theta=-\dfrac{3\pi}{4}+2k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\text{It's not equal to}\ \dfrac{\pi}{4}\ \text{for any value of }\ k.

7 0
2 years ago
A water balloon is thrown out of a window 96 feet above the ground. The balloon is traveling downward at 16 feet per second init
Marysya12 [62]

Answer:

3 seconds.

Step-by-step explanation:

Since we are figuring out when the water balloon will hit the ground, y will need to be equal to 0.

0 = - 16t² - 16t + 96

Now we simply factor the trinomial to find t.

0 = -16(t² - t - 6)

0 = (t - 3)(t + 2)

t - 3 = 0 ⇒ t = 3

t + 2 = 0 ⇒ t = -2

Since we are referring to time, we need to use the positive value. Therefore, the water balloon will take 3 seconds to hit the ground.

6 0
3 years ago
Read 2 more answers
Please help me I will mark BRAINLIEST!!! Find the value of x
Basile [38]

Answer:

  x = 2√3 ≈ 3.464

Step-by-step explanation:

The side marked x is opposite the given 30° angle. The side marked 6 is adjacent to that angle. The trig function relating opposite and adjacent sides of a right triangle is ...

  Tan = Opposite/Adjacent

Filling in values, we have ...

  tan(30°) = x/6

Multiplying by 6 gives ...

  x = 6tan(30°) = 6(√3/3)

  x = 2√3 ≈ 3.464

6 0
2 years ago
Find the probability distribution for the following function: P(x)=x/2+1 for x=4,6, and 8
son4ous [18]
56 because i just took the test ps this is wrong i just need the points
4 0
2 years ago
Verify which of the following are identities.
-Dominant- [34]

Answer:

Only the second equation is an identity

Step-by-step explanation:

$8 \frac{\tan^2(\theta)}{\sec(\theta)} \csc^2(\theta)=8 \csc(\theta)$

<u>Note that </u>

\tan^2(\theta)\csc^2(\theta)=\sec^2(\theta)

<u>You can confirm it: </u>

$\frac{\sin^2(\theta)}{\cos^2(\theta)}\cdot    \frac{1}{\sin^2(\theta)}= \frac{1}{cos^2(\theta)}= \sec^2(\theta)$

<u>Therefore</u>

$8 \frac{\sec^2(\theta)}{\sec(\theta)} =8 \csc(\theta)$

$8 \frac{\sec(\theta)}{1} =8 \csc(\theta)$

8\sec(\theta)=8\csc(\theta)

<h2>It is not an Identity</h2>

<u>Let's the second one</u>

$13 \frac{\tan^2(\theta)}{\sec(\theta)} \csc^2(\theta)=13\sec(\theta)$

In this case, we already performed the calculations, so it is true. It is an Identity.

3 0
2 years ago
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