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3 years ago

(1). Simplify.

Mathematics

2 answers:

Brut [27]3 years ago

7 0

$22 \div (9 + 2) = 2$
22/11
=2

Akimi4 [234]3 years ago

7 0

Answer:

1) $22\div (9+2)=2$

2) $8+3\cdot 42=134$

3) Option A - $(12+6)\div(3+3)$

4) Option D - $(75-5)\times 1+4$

Step-by-step explanation:

1) Simplify $22\div (9+2)$

Solution :

Add the terms in bracket,

$22\div (9+2)=22\div 11$

Divide,

$22\div (9+2)=2$

2) Evaluate $8+3\cdot 42$

Solution :

Solve the dot product,

$8+3\cdot 42=8+126$

Add the terms,

$8+3\cdot 42=134$

3) Which expression has a value of 3?

Solution : Solve each expression,

A. $(12+6)\div(3+3)$

$(12+6)\div(3+3)=18\div 6=3$

B. $(12+6)\div3+3$

$(12+6)\div3+3=18\div 3+3=6+3=9$

C. $12+6\div(3+3)$

$12+6\div(3+3)=12+6\div 6=12+1=13$

D. $12+(6\div3+3)$

$12+(6\div3+3)=12+(2+3)=12+5=17$

Option A is correct.

4) Which expression has a value of 74?

Solution : Solve each expression,

A. $(75-5)\times(1+4)$

$(75-5)\times(1+4)=70\times 5=350$

B. $75-5\times(1+4)$

$75-5\times(1+4)=75-5\times 5=75-25=50$

C. $75-(5\times1+4)$

$75-(5\times1+4)=75-(5+4)=75-9=66$

D. $(75-5)\times 1+4$

$(75-5)\times 1+4=70\times 1+4=70+4=74$

Option D is correct.

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Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

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We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

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s = sample standard deviation = 15.1 lb

n = sample of cables = 45

$\mu$ = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

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P(-2.02 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.02) = 0.95

P( $-2.02 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }$ , $768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }$ ]

= [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

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