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ser-zykov [4K]
3 years ago
7

The three sides of a triangle are 4cm, 6cm and 8cm.

Mathematics
1 answer:
yarga [219]3 years ago
6 0

Answer:

In bold below.

Step-by-step explanation:

(a) The largest angle is opposite the largest side.

So by the Cosine Rule:

8^2 = 4^2 + 6^2 - 2*4*6 cos x

cos x =  (8^2 - 4^2 - 6^2) / (-2*4* 6)

= -0.25.

x = 104.48 degrees.

(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48

= 11.62

= 3 √15.

(c)  The shortest altitude will have the longest sides as the base.

Area = 1/2 * altitude * base

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

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Find the circumference of the circle
vaieri [72.5K]

Answer:

72.22

Step-by-step explanation:

4 0
3 years ago
A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken
mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

X=1 number of citrus trees that are infected with the citrus red mite.

n=5 random sample taken

\hat p=\frac{1}{5}=0.2 estimated proportion of citrus trees that are infected with the citrus red mite.

p true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values would be given by:

t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.01 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56  

And rounded up we have that n=6147

5 0
3 years ago
Whats 318,224,475 rounded too the nearest ten.​
aivan3 [116]
318,224,480

5 is in the ones place so u round up
8 0
3 years ago
What is the distance between (5, -1) and (5,-4)
jarptica [38.1K]

Answer:

Step-by-step explanation:

To evaluate for such, the following comprehension is required,

Equation Required: Distance Formula: d(P, Q) = √ (x2 − x1)^2 + (y2 − y1)^2

Denote the configurations as the following,

(5, -1). (5, -4)

X1 Y1. X2. Y2

D(P, Q) = √(5 - 5)^2 + (-4 +1)^2. <== Since the double negative is present, the operation is acknowledged as positive.

D(P, Q) = √(0)^2 + (-3)^2

D(P, Q) = √9 = 3

Thus, the agglomerate distance between the points situated in the Cartesian plane is disclosed, and is, henceforth, disseminated as 03 units.

3 0
2 years ago
A 2 pint jug costs $2.28 what is the price per cup?
USPshnik [31]

Answer:

0.57

Step-by-step explanation:

a 2 pint jug costs $2.28

2 pints=4 cups

$2.28/4=0.57

6 0
3 years ago
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