All categories

2 years ago

Calculate the length of the side of the square to 1dp.

Mathematics

1 answer:

Sveta_85 [38]2 years ago

8 0

Answer:

72 cm

Step-by-step explanation:

You can solve this problem using the properties of the 45-45-90 right triangle. Assuming the 12 cm is a diagonal of the square, each side of the square can be modeled as x, and the diagonal will be x $\sqrt{2}$ .

This means $x\sqrt{2} =12$ , so $x=\frac{12}{\sqrt{2} }$ .

Next, to find the area of the square you take the square of any of its sides. Since x is the length of one side, and $x=\frac{12}{\sqrt{2} }$ , you can square $\frac{12}{\sqrt{2} }$ to get the area. This is equal to $\frac{144}{2}$ or 72 cm.

You might be interested in

Two cyclists leave a city at the same time, one going east and the other going west. The westbound cyclist bikes at 3 mph faster

NikAS [45]

We will say that the eastbound cyclist is going x mph. This means that the westbound cyclist is going x+3 mph.
They are both cycling for 6 hours and end up 162 miles apart.
Distance=rate*time
6x+6(x+3)=162
6x+6x+18+162
12x=144
x=12
So, the eastbound cyclist is going 12 mph.
Remember the westbound cyclist is going 3 mph faster, so s/he is going 15 mph.
Hope this helps!!

7 0

3 years ago

12 A train in France can travel at a speed

mylen [45]

Answer: 267.402

Step-by-step explanation:

The answer is 267.402 because 217.4 times 1.23 = 267.402.

4 0

3 years ago

Read 2 more answers

3) Lane and Zack purchased a house for $245,000 in 2016. The house loses 4% of its value each year,

kherson [118]

Answer:

In 2030 Lane & Zack's house be worth $65,739.27.

Step-by-step explanation:

Here, as we know The value of property = $245,000

Rate of depreciation = 4% of its present value

Time = From 2016 to 2030 = 14 years

Now, here: Amount depreciated = -( COMPOUND INTEREST on the value)

<u> Step 1: CALCULATE THE COMPOUND INTEREST on P = $245,000</u>

$A = P(1 + \frac{r}{100} )^t\\\implies A = (245,000)(1 + \frac{4}{100} )^{14} = (245,000)(1 + \frac{4}{100} )^{14}\\=245,000 (\frac{104}{100} )^{14} = 424,260.73$

or, AMOUNT = $424,260.73

Now, AMOUNT = Compound I + Principal

⇒Compound I = A - P = $424,260.73 - $245,000 =$ 179,260

So, the amount of the house by which house depreciates = $ 179,260

⇒The depreciated value = Actual Value - The depreciated amount

= $245,000 - 179,260 = $65,739.27

Hence, in 2030 Lane & Zack's house be worth $65,739.27.

4 0

3 years ago

We saw two distributions for triathlon times: N (μ = 4313, σ = 583) for Men, Ages 30 - 34 and N (μ = 5261, σ = 807) for the Wome

irakobra [83]

Answer:

Step-by-step explanation:

Hello!

Using the information of the triathlon times of men and women you have to find:

a. The cutoff time for the fastest 5% men, if the times of the male triathletes have a normal distribution, this value will separate the top 5% from the rest of the distribution, symbolically:

P(X≥x₀)= 0.05

Where x₀ represents the cutoff time that you need to find.

Now if this value has 5% of the distribution above it, then 95% of the distribution will be below it, symbolically:

P(X<x₀)= 0.95

Next is to use the standard normal distribution, you have to find the Z value that accumulates 0.95 of probability: P(Z<z₀)= 0.95

z₀= 1.648

Using the formula: Z= (X-μ)/δ what is left to do is to reverse the standardization and reach the value of the variable:

z₀= (x₀-μ)/δ

x₀= (z₀*δ)+μ

x₀= (1.648*583)+4313

x₀= 5273.784 seconds

The cutoff time for the fastest 5% is 5273.784 seconds.

b. The cutoff time for the slowest 10% women, if you are taking the "slowest" into account, then this is the lowes 10% of the distribution. Meaning that the value of time separates the "lowest" 10% of the distribution from the rest, symbolically:

P(X≤x₀)=0.10

Same as before, you have to use the standard normal distribution:

P(Z≤z₀)= 0.10

z₀= - 1.283

Now using this value you have to reverse the standardization:

z₀= (x₀-μ)/δ

x₀= (z₀*δ)+μ

x₀= (-1.283*807)+5261

x₀= 4225.619 seconds

The cutoff time for the slowest 10% is 4225.619 seconds.

I hope it helps!

7 0

3 years ago

Mata soccer practice on May 4 he will practice every fourth day after that tent begins baseball practice on May 3 and continuous

Murrr4er [49]

Answer:

May 4th

The pattern goes like this

May 4th, May 8th, May 12th, May 16th, ...

3 0

3 years ago

Calculate the length of the side of the square to 1dp.​

Calculate the length of the side of the square to 1dp.