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3 years ago

Please help asap!! Will give brainlist :)

Mathematics

1 answer:

Nostrana [21]3 years ago

5 0

Answer:

44 in²

Step-by-step explanation:

The figure is composed of a triangle, a rectangle and a trapezium.

Area of the triangle = $\frac{1}{2}$ bh = $\frac{1}{2}$ × 3 × 4 = 6 in²

Area of the rectangle = lb = 10 × 3 = 30 in²

Area of trapezium = $\frac{1}{2}$ h (a + b)

where h is the height and a, b the parallel bases, thus

area of trapezium = $\frac{1}{2}$ × 2 × (5 + 3) = 1 × 8 = 8 in²

Total area = 6 in² + 30 in² + 8 in² = 44 in²

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<h3>Slope of a function</h3>

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3 years ago

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3 years ago

Read 2 more answers

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ANEK [815]

Answer:

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Step-by-step explanation:

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3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.65 millimeters and a standard deviat

nexus9112 [7]

Answer:

Two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.

Step-by-step explanation:

We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.65 millimeters and a standard deviation of 0.07 millimeters.

<em>Let X = diameters of bolts produced in a machine shop</em>

So, X ~ N( $\mu=5.65,\sigma^{2} = 0.07^{2}$ )

The z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean

$\sigma$ = standard deviation

<u>Now, we have to find the two diameters that separate the top 4% and the bottom 4%.</u>

Firstly, Probability that the diameter separate the top 4% is given by;

P(X > x) = 0.04

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-5.65}{0.07}$ ) = 0.04

P(Z > $\frac{x-5.65}{0.07}$ ) = 0.04

<em>So, the critical value of x in z table which separate the top 4% is given as 1.7507, which means;</em>

$\frac{x-5.65}{0.07}$ = 1.7507

$x-5.65 = 0.07 \times 1.7507$

$x$ = 5.65 + 0.122549 = 5.77

Secondly, Probability that the diameter separate the bottom 4% is given by;

P(X < x) = 0.04

P( $\frac{X-\mu}{\sigma}$ < $\frac{x-5.65}{0.07}$ ) = 0.04

P(Z < $\frac{x-5.65}{0.07}$ ) = 0.04

<em>So, the critical value of x in z table which separate the bottom 4% is given as -1.7507, which means;</em>

$\frac{x-5.65}{0.07}$ = -1.7507

$x-5.65 = 0.07 \times (-1.7507)$

$x$ = 5.65 - 0.122549 = 5.53

Therefore, the two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.

4 0

3 years ago