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3 years ago

Jessica has 20 chocolates. After 4 hours, she has 12 chocolates. How many chocolates does she eat per hour?

Mathematics

2 answers:

taurus [48]3 years ago

7 0

She easy 2 pieces per hour

irina [24]3 years ago

5 0

Answer: Jessica eats 2 chocolates an hour.

Step-by-step explanation: To find how many she eats in hour, we would first subtract the number of chocolates by the number that are left (20 - 12), which equals 8. Next, we would divide the total by the time spent eating (8 / 4), or 2.

Consider marking this answer brainliest if it helped you out.

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Prove that:

Lorico [155]

A.)

$\csc^2(x) \tan^2 (x)- 1 = \tan^2(x)$

Use the identities $\csc x = 1 / \sin x$ and $\tan x = \sin x / \cos x$ on the left-hand side

$\begin{aligned}
\text{LHS} &= \csc^2(x) \tan^2 (x)- 1 \\
&= \frac{1}{\sin^2 (x)} \cdot \frac{\sin^2 (x)}{\cos^2 (x)} - 1 \\
&= \frac{1}{\cos^2 (x)} - 1
\end{aligned}$

Make 1 have a common denominator to allow for fraction subtraction
Multiply the numerator and denominator of 1 by cos^2 x

$\begin{aligned} \text{LHS} &= \frac{1}{\cos^2 (x)} - 1 \cdot \tfrac{\cos^2 (x)}{\cos^2 (x)} \\
&= \frac{1}{\cos^2 (x)} - \frac{\cos^2 (x)}{\cos^2 (x)} \\
&= \frac{1 - \cos^2 x}{\cos^2 (x)}
\end{aligned}$

Use Pythagorean identity for the numerator.

If $\sin^2 (x) + \cos^2(x) = 1$ then subtracting both sides by $\cos^2 (x)$ yields $\sin^2(x) = 1 - \cos^2(x)$ . We can substitute that into the numerator

$\begin{aligned} \text{LHS} &= \frac{1 - \cos^2 (x)}{\cos^2 (x)} \\
&= \frac{\sin^2 (x)}{\cos^2 (x)} \\
&= \tan^2 (x) && \text{Since } \tan x = \tfrac{\sin x }{\cos x} \\
&= \text{RHS}
\end{aligned}$

======

b.)

$\dfrac{\sec(x)}{\cos(x)} - \dfrac{\tan(x)}{\cot(x)} = 1$

For the left-hand side:
By definition, $\sec(x) = 1/\cos(x)$ and $\tan (x) = 1/\cot (x)$

$\begin{aligned}
\text{LHS} &= \dfrac{\sec(x)}{\cos(x)} - \dfrac{\tan(x)}{\cot(x)} \\
&= \dfrac{ \frac{1}{\cos(x)} }{\cos(x)} - \dfrac{\frac{1}{\cot(x)}}{\cot(x)} \\
&= \frac{1}{\cos^2 (x)} - \frac{1}{\cot^2(x)} 
\end{aligned}$

Since $\cot (x) = \cos (x) / \sin (x)$

$\begin{aligned} \text{LHS} &= \frac{1}{\cos^2 (x)} - \frac{1}{\frac{\cos^2(x)}{\sin^2(x)} } \\ &= \frac{1}{\cos^2 (x)} -\frac{\sin^2(x)}{\cos^2(x)} \\ &= \frac{1 - \sin^2(x)}{\cos^2 (x)} \end{aligned}$

Using Pythagorean identity, $\cos^2(x) = 1 - \sin^2(x)$ so

$\begin{aligned} \text{LHS} &= \frac{\cos^2(x)}{\cos^2 (x)} \\
&= 1 \\
&= \text{RHS}
\end{aligned}$

6 0

3 years ago

Tx+12y=-3

Lisa [10]

In form
ax+by=c
slope=-a/b

a=T
b=12
slopt=-10
-10=-T/12
multiply both sides by 12
-120=-T
mulitply -1
120=t

T=120

3 0

3 years ago

Read 2 more answers

The cost of a coffee maker is $76.70 the markup is 20% of the cost. What is the selling price of the coffee maker?

Dmitrij [34]

Answer: The selling price of the coffee maker is $92.04

If the original cost is $76.70 but the company wants to make profit from the product, meaning they want to sell it higher than what they purchased it for in order to gain money, then you add the markup cost to the original cost (20%).

$76.70 + 20% of $76.70

=$76.70 + $15.34

=$92.04 selling price of coffee maker.

5 0

4 years ago

Read 2 more answers

Whoever answers first i will mark as brainiest

vfiekz [6]

Answer:

As shown in picture,

volume of cone V = base area x height x (1/3) = pi x (4/2)^2 x 6 x (1/3) = 8 x pi

volume of cup V = base area x height = pi x (3/2)^2 x 3 = 6.75 x pi

(all the volumes are in cubic inches)

A - Incorrect

24 pack of cups: V = 24 x 6.75 x pi = 162 x pi

21 pack of cones: V = 21 x 8 x pi = 168 x pi

162 x pi < 168 x pi

B - Correct

12 pack of cups: V = 12 x 6.75 x pi = 254.5 > 250

C - Correct

14 pack of cones: V = 14 x 8 x pi =351.9 > 350

D - Correct

Volume of cylinder 8 tall, 6 wide: V = pi x (6/2)^2 x 8 = 72 x pi

12 pack of cups: V = 12 x 6.75 x pi = 80.4 x pi > 72 x pi

Hope this helps!

7 0

3 years ago

A set of data has a mean of 45.6 what is the mean if 5.0 is added to each score

Solnce55 [7]

Answer:

The mean will be increased by 5

Step-by-step explanation:

Suppose a set of data $(2, 4, 6, 8, 10, 12)$

Mean is defined as sum of all the values given set of data divided by total number of values.

Mean1 = $\frac{2+4+6+8+10+12}{6} = \frac{42}{6} = 7$

Now if we add 5 toeach value, the new set becomes $(7, 9, 11, 13, 15, 17)$

for which,

Mean2 = $\frac{7+9+11+13+15+17}{6} = \frac{72}{6} = 12$

Mean2 - Mean1 = 5

4 0

3 years ago