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Delicious77 [7]
3 years ago
14

The pyrotechnic team for Fist Bump’s tour want to know how high the arena is to 2 decimal places. The arena is 61.3786 metres hi

gh. How high is it to 2 d.p?
Mathematics
1 answer:
Aloiza [94]3 years ago
4 0
When you find any value to x amount of decimal places, you need to go to the term AFTER that to determine the correct value.  So, for this, take 61.378 metres.  From here, look if the last number is 4 or less.  If the number is 4 or less, take the leftmost number off, and you will have your answer (if we had 61.373, the correct answer would be 61.37).  If the number is 5 or more, take the leftmost number off, and add 1 to the new leftmost number.  Since the last number is 8, the correct answer here is 61.38 metres high.  If adding 1 makes the number 10, keep the 0 at the end.  So, if you had 61.399, you would make it 61.40
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Descent, Inc., produces a variety of climbing and mountaineering equipment. One of its products is a traditional three-strand cl
Rainbow [258]

Solution :

Assuming $\sigma_1^2=\sigma_2^2$

We have to test

$H_0:\mu_1=\mu_2$

Against H_a: \mu_1 \neq \mu_2

Level of significance, $\alpha = 0.05$

$s_p=\sqrt{\frac{(n_1-1)s_1^2+ (n_2-1)s_2^2}{n_1+n_2-2}}$

$s_p=\sqrt{\frac{(25-1)(425)^2+ (20-1)(415)^2}{25+20-2}}$

   = 420.6107

Under H_0, the t-statistics is as follows:

$t=\frac{(\overline{x_1} - \overline{x_2})}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \sim $             $\text{t with }(n_1+n_2-2) \ DF$

$t=\frac{(7200-7087)}{(420.6107)\sqrt{\frac{1}{25}+\frac{1}{20}}}$

 = 0.90

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    = 43

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3 0
3 years ago
Find the volume of the garden shed
Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}

Therefore:

\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}

<h3><u>Volume of the garden shed</u></h3>

\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}

6 0
1 year ago
Read 2 more answers
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