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Gnom [1K]
3 years ago
8

(14-8) × (15-4) Use the order of operations to find the value of each expression

Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

66

Step-by-step explanation:

the order of operations is the acronym PEMDAS which stands for:

P: Parentheses

E: Exponents

M & D: Multiplication and Division

A & S: Addition and Subtraction

we do these in order, from left to right in the equation

for the equation (14 - 8) x (15 - 4), we would start with solving the parentheses

there are 2 sets of parentheses, so we will go from left to right in solving it:

(14 - 8) = 6

(15 - 4) = 11

we replace the values we have found from the parentheses into the equation

6 x 11

now we go through the list

we can already eliminate exponents because there are none in this equation

the next step is multiplication & division, in this equation there is only multiplication, so we multiply 6 x 11 which gives us the answer 66

there is nothing left for us to do at this point, so 66 is our final answer

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The manufacturer of hardness testing equipment uses​ steel-ball indenters to penetrate metal that is being tested.​ However, the
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Answer:

Check the explanation

Step-by-step explanation:

Let X denotes steel ball and Y denotes diamond

\bar{x_1} = 1/9( 50+57+......+51+53)

=530/9

=58.89

\bar{x_2}= 1/9( 52+ 56+....+ 51+ 56)

=543/9

=60.33

difference = d =(60.33- 58.89)

=1.44

s^2=1/n\sum xi^2 - n/(n-1)\bar{x}^2

s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2

=31686/8 - 9/8( 3468.03)

=3960.75 - 3901.53

=59.22

s1 = 7.69

s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2

=33295/8 - 9/8 (3640.11)

=4161.875 - 4095.12

=66.75

s2 =8.17

sample standard deviation for difference is

s=\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}

 = \sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}

= \sqrt{1007.76/16}

=7.93

sd = s*\sqrt{(1/n1)+(1/n2)}

=7.93*\sqrt{(1/9)+(1/9)}

=7.93* 0.47

=3.74

For 95% confidence level Z (\alpha /2) =1.96

confidence interval is

d\pm Z(\alpha /2)*s_d

=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)

=(1.44 - 7.35 , 1.44 + 7.35)

=(-2.31, 8.79)

There is sufficient evidence to conclude that the two indenters produce different hardness readings.

3 0
3 years ago
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