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Step2247 [10]
3 years ago
5

Reduce to the simplest form. -9/6 + (-3/5)

Mathematics
1 answer:
creativ13 [48]3 years ago
5 0

Answer:

-\frac{21}{10} or -2.1 (they're the same)

Step-by-step explanation:

  1. Simplify: -\frac{9}{6} + (-\frac{3}{5}) = -\frac{9}{6} - \frac{3}{5}  
  2. Find a common denominator. The LCM of 6 and 5 is 30, so multiply the numerator and the denominator by the same thing: 6 × 5 = 30, -9 × 5 = -45, 5 × 6 = 30, 3 × 6 = 18
  3. Write the new fractions: -\frac{45}{30} - \frac{18}{30}  
  4. Subtract: -45/30 - 18/30 = -\frac{63}{30} = -\frac{21}{10}

I hope this helps!

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A 15% percent markup means that the typewriter cost was increased by 15%, or 0.15 by moving the decimal 2 places to the left. If the original price was x, and 15% of it is 0.15*x, we can add them up to get 1.15*x=129.95. Dividing both sides by 1.15, we get x=113 dollars
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3 years ago
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Jane multiplies her number by three and subtracts 2.
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Answer:

Let the number they chose be 'x'.

Result of Jane = 3x -2

Result of Elliot = 2x+3

Given that,

The product of their result = 110

or, (3x-2)(2x+3) = 110\\or, 6x^{2} +9x-4x-6 = 110\\or, 6x^{2} +5x - 6 = 110\\or, 6x^{2} +5x - 6-110 = 0\\\\or, 6x^{2} +5x - 116 = 0\\or, 6x^{2} +29x - 24x - 116 = 0\\or, x (6x +29) -4(6x+29) = 0\\or, (x-4)(6x+29) = 0\\i.e. x=4 or x=\frac{-29}{6} \\So,~ the ~number ~they~ chose~was ~either ~4 ~or ~\frac{-29}{6}

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2 years ago
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From pre
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Answer:

Null Hypothesis, H_0 : \mu \leq 250 W  

Alternate Hypothesis, H_A : \mu > 250 W    

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

<u><em>Let </em></u>\mu<u><em> = mean power consumption of microwave ovens.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 250 W  

Alternate Hypothesis, H_A : \mu > 250 W    

Here, <u>null hypothesis states tha</u>t the mean power consumption of microwave ovens is no more than 250 W.

On the other hand, <u>alternate hypothesis sates that</u> the mean power consumption of microwave ovens is more than 250 W.

The test statistics that would be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;

                       T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.

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