20 points . Please answer

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

I need help on solving these types of geometry problems! Teacher said the answer is 7 but I have to show work. Thank you!

Nikolay [14]

The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.

This means

$82^\circ=m\angle 2$

$\implies82=10x+12$

$\implies10x=70$

$\implies\boxed{x=7}$

4 0

3 years ago

Pls help fast maths

-Dominant- [34]

Answer:

the answer of question number 4 is : (x+4)

6 0

2 years ago

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is .5

lara [203]

Answer:

7.3% of the bearings produced will not be acceptable

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 0.499, \sigma = 0.002$

Target value of .500 in. A bearing is acceptable if its diameter is within .004 in. of this target value.

So bearing larger than 0.504 in or smaller than 0.496 in are not acceptable.

Larger than 0.504

1 subtracted by the pvalue of Z when X = 0.504.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.504 - 0.494}{0.002}$

$Z = 2.5$

$Z = 2.5$ has a pvalue of 0.9938

1 - 0.9938= 0.0062

Smaller than 0.496

pvalue of Z when X = -1.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.496 - 0.494}{0.002}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.0668 + 0.0062 = 0.073

7.3% of the bearings produced will not be acceptable

4 0

3 years ago

What is 2 gallons minus 5 quarts

MariettaO [177]

There are 4 quarts in a gallon.
In two gallons would be 8 quarts.

2 gallons - 5 quarts = 8 quarts - 5 quarts = 3 quarts.

Note: 3 quarts is 3/4 or .75 of a gallon.

6 0

3 years ago