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3 years ago

Geometry

Mathematics

1 answer:

trapecia [35]3 years ago

4 0

Answer:

EF = 8

Step-by-step explanation:

The following data were obtained from the question:

EF = 2x

FG = 8

EG = 4x

EF =?

To obtain the value of EF, we shall first, obtain the value of x. This can be obtained as follow:

EG = EF + FG

EF = 2x

FG = 8

EG = 4x

4x = 2x + 8

Collect like terms

4x – 2x = 8

2x = 8

Divide both side by 2

x = 8/2

x = 4

Therefore, the value of x is 4.

Finally, we shall determine the the value of EF as follow:

EF = 2x

x = 4

EF = 2x

EF = 2(4)

EF = 8

**** Check ****

EG = EF + FG

EF = 2x

EG = 4x

FG = 8

4x = 2x + 8

x = 4

4(4) = 2(4) + 8

16 = 8 + 8

16 = 16

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3 years ago

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3 years ago

Read 2 more answers

A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25. Compute the probability t

Sophie [7]

Answer:

(1) The probability that the sample mean is Greater than 59 = 0.778

(2) The probability that the sample mean is less than 59 = .3632

(3) The probability that the sample mean is is Between 54 and 59 = 0.559

Step-by-step explanation:

Given -

Mean $(\nu )$ = 55

Standard deviation $(\sigma )$ = 14

Sample size ( n ) = 25

the probability that the sample mean $(\overline{X})$ is Greater than 59 =

$P(\overline{X} > 59 )$ = $P(\frac{\overline{X} - \nu}{\frac{\sigma}{\sqrt{n}}} > \frac{59 - 55 }{\frac{14}{\sqrt{25}}})$

= $P(Z > 1.428 )$

= 1 - $P(Z < 1.428 )$

= 1 - 0.9222 = .0778

the probability that the sample mean $(\overline{X})$ is Less than 54 =

$P(\overline{X}< 54 )$ = $P(\frac{\overline{X} - \nu}{\frac{\sigma}{\sqrt{n}}} < \frac{54 - 55 }{\frac{14}{\sqrt{25}}})$

= $P(Z< -.357 )$

= .3632

the probability that the sample mean is Between 54 and 59 =

$P(54< \overline{X}< 59)$ = $P(\frac{54 - 55 }{\frac{14}{\sqrt{25}}}< \frac{\overline{X} - \nu}{\frac{\sigma}{\sqrt{n}}} < \frac{59 - 55 }{\frac{14}{\sqrt{25}}})$