MATHEMATICS MIDDLE SCHOOL

What is 4 2/10 - 2 8/10

Answers

Answer 1

Answer:

Answer: 7/5 or 1 2/5

Step-by-step explanation:

Look at attachment

Answer 2

Answer:

Answer:1.4

Step-by-step explanation: 4 2/10 - 2 8/10=1.4

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Quinn returned home one summer's day to find it sweat-inducingly hot! He turned the air conditioner on and fell asleep. The room's temperature decreased by 0.5° Celsius each minute, and Quinn woke up 60 minutes later when it was 10° Celsius.

Answers

Answer:

He went to bed when it was 40 celsius

Step-by-step explanation:

.5 degree per minute for 60 minutes

.5*60

30 degrees more

30+10=40 degrees

Which is bigger 5/8 or 7/12

Answers

5/8=0.625

7/12=0.583......

5/8 is bigger as ive put both into a decimal as it is easier to tell

5/8 and 7/12
15/24 14/24
15 is greater than 14

30-[(9x2)-(3x4)] numerical expression ;)

Answers

30-[(9x2)-(3x4)]
30-[18-(3x4)]
30-(18-12)
30-6
24

$30-[(9*2)-(3*4)]$
$30-(18-12)$
$30-6$
$24$
The answer is:24

Mrs. Cleaver mixes 1.24 liters of red paint with 3 times as much blue paint to make purple paint. She pours the paint equally into 5 containers. How much BLUE paint is in each container? Give your answer in liters.

Answers

The amount of blue paint in each container is $\fbox{\begin\n\ 0.744 liters \end{minispace}}$ .

Further explanation:

The mixture mixed by Mrs. Cleaver contains 1.24 litres of red paint with 3 times blue paint to obtain purple paint.

So, the amount of blue paint is calculated as,

${3} * {1.24}=3.72 \text { liters}$

Therefore, the total amount of paint mixture is the sum of blue paint and red paint.

$\fbox{\begin \n\begin{aligned} \text{Total paint}= 1.24+3.72\n=4.96 \text{ liters}\n\end{aligned}\n\end{minispace}}$

Now, as Mrs. Cleaver divides the paint mixture equally in 5 containers so the amount of paint in one container is calculated as,

$\boxed{\begin{aligned}\text{Amount of paint in one container}&= (4.96)/(5)\n &=0.992 \text{ liters} \end {aligned}}$

Since amount of blue paint mixed is three times the red paint so the fraction of blue paint to the total paint is $(3)/(4)$ .

Now, as it is known that the fraction of blue paint to the total paint is $(3)/(4)$ and the amount of paint in a container is $0.992 \text{ liters}$ then the blue paint in one container is calculated as,

$\boxed{\begin{aligned}\text{Blue paint in one container} =(3)/(4) * 0.992\n=0.248 \text{ liters}\end{aligned}}$

Thus, the amount of blue paint in each of the five containers is $\fbox{\begin\n\ 0.744 liters \end{minispace}}$ .

Learn more:

1. To solve one variable linear equation brainly.com/question/1682776

2. Linear equation application brainly.com/question/2479097

3. Composite functions brainly.com/question/2142762

Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Mixtures and ratios

Keywords: mixture, paint, red paint, blue paint, Mrs. Cleaver, purple paint, fraction, each container, five containers, divides, times, equally divide, mixes, liters.

.744 liters
hope this helped :D

3.72/5 = .744 liters

If 3 tan θ = 1, then find the value of sin2 θ –
cos2
θ.

Answers

Final answer:

Firstly, express tan θ as sin θ/cos θ, then use the Pythagorean identity to find sin2 θ and cos2 θ. Solve for sin2 θ and cos2 θ using the given tan θ. The final result is sin2 θ - cos2 θ = -4/5.

Explanation:

If 3 tan θ = 1, then to find the value of sin2 θ − cos2 θ, you first need to express tan θ in terms of sine and cosine, which gives you tan θ = sin θ/cos θ. Now, since 3 tan θ = 3 (sin θ/cos θ) = 1, then sin θ/cos θ = 1/3.

To find sin2 θ and cos2 θ, you can use the Pythagorean identity, 1 = sin2 θ + cos2 θ. We already have a value for tan θ, which allows us to solve for sin θ and cos θ individually. From sin θ/cos θ = 1/3, you can cross multiply to find that sin θ = cos θ / 3. Now, if you square both sides of the equation, you'll get sin2 θ = (cos θ)2 / 9.

Using the Pythagorean identity, let cos2 θ = x, then sin2 θ = x/9, and according to the identity, x + x/9 = 1, or 10x/9 = 1, which implies x = 9/10. Therefore, sin2 θ = (9/10)/9 = 1/10 and cos2 θ = 9/10. Finally, sin2 θ - cos2 θ = 1/10 - 9/10 = -8/10 or -4/5.