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2 years ago

12

Find the value of the variable in the parallelogram. RZ = 4x + 2 SW=9x - 8 X=

1 answer:

ipn [44]2 years ago

8 0

Answer:

$x=12$

Step-by-step explanation:

This parallelogram contains a right angle. This tells us that the parallelogram is a rectangle.

The diagonals in a parralelogram bisect each other.

The diagonals in a rectangle are congruent.

$RZ+ZT=RT\\(4x+2)+(4x+2)=RT\\8x+4=RT$

$RT=SW\\8x+4=9x-8\\4=x-8\\x=12$

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Whats the difference of squares

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An example of the difference of squares would be: a^2-b^2 = (a+b)(a-b)

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3 years ago

KonstantinChe [14]

Answer:

the last choice: 4 ft, 4 ft, 10 ft

Step-by-step explanation:

prism A: 8x4x5 = 160

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3 years ago

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

a

$\= x = 18.5$ , $\sigma = 5.15$

b

$15.505 < \mu < 21.495$

c

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

A whale-watching tour boat cannot operate if the total passenger weight is more than 3 comma 150 comma 000 grams. What is the m

Andru [333]

Answer:

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Step-by-step explanation:

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4 years ago

Please solve this question

oee [108]

Answer:

$\frac{1}{81}$

Step-by-step explanation:

Using the rule of exponents

$a^{-m}$ ⇔ $\frac{1}{a^{m} }$

Evaluating from the inside parenthesis outwards

$(-\frac{1}{3}) ^{2}$ = - $\frac{1}{3}$ × - $\frac{1}{3}$ = $\frac{1}{9}$ , then

$(\frac{1}{9}) ^{-2}$ = $\frac{1}{9^{-2} }$ = 9² = 81 , then

$(81)^{-1}$ = $\frac{1}{81}$

4 0

3 years ago