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4 years ago

Solve x - 3 1/8 = 5/12

Mathematics

1 answer:

Anna007 [38]4 years ago

7 0

Answer:

$\large\boxed{x=\dfrac{85}{24}=3\dfrac{13}{24}}$

Step-by-step explanation:

Convert the mixed number to the fraction:

$3\dfrac{1}{8}=\dfrac{3\cdot8+1}{8}=\dfrac{25}{8}$

METHOD 1:

$x-3\dfrac{1}{8}=\dfrac{5}{12}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\\\\\text{the common denominator is 24}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\qquad\text{multiply both sides by 24}\\\\24x-(3)(25)=(2)(5)\\\\24x-75=10\qquad\text{add 75 to both sides}\\\\24x=85\qquad\text{divide both sides by 24}\\\\\boxed{x=\dfrac{85}{24}}$

METHOD 2:

$x-3\dfrac{1}{8}=\dfrac{5}{12}\qquad\text{add}\ 3\dfrac{1}{8}\ \text{to oboth sides}\\\\x=\dfrac{5}{12}+3\dfrac{1}{8}\\\\x=\dfrac{5\cdot2}{12\cdot2}+3\dfrac{1\cdot3}{8\cdot3}\\\\x=\dfrac{10}{24}+3\dfrac{3}{24}\\\\x=3\dfrac{10+3}{24}\\\\\boxed{x=3\dfrac{13}{24}}$

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A smart phone costs $149.99 before tax. The tax on the smart phone is 7%.

pochemuha

Answer:TC=$160.49

Step-by-step explanation:total cost=original+tax

tax=7% of 149.99

tax=0.07 times 149.99

tax=10.49993

total cost=149.99+10.49993

total cost=160.4893

round

sooo TC=$160.49

6 0

3 years ago

Maple town is 16 kilometers due north of the airport and sachet town is due east of the airport. The shortest distance between m

Alexxandr [17]

Answer:

Sachet town is 12km from the airport

Step-by-step explanation:

In this question, we are asked to calculate the distance from sachet town to the airport.

This can be calculated by referring to a diagrammatic representation. Please check attached file.

Let’s proceed with the calculations however.

From the question, we can see that we have formed a Right angled triangle from the diagram and we need to calculate the distance x.

Mathematically;

x^2 + 16^2 = 20^2

x^2 = 20^2 - 16^2

x^2 = 400 - 256

x^2 = 144

x = sq.rt of 144

x = 12km

6 0

4 years ago

Read 2 more answers

How is 2 ones the same has 20 tenths

GalinKa [24]

They are the same because tenths are 1/10 of ones. So if you had 20 tenths, you could multiply 20and 1/10. When you do that you get 20/10 which in simplest form is 2 ones. If you do the opposite of 2 to 20, you get the same thing.

6 0

4 years ago

Read 2 more answers

A. Student GPAs: Bob’s z-score z = + 1.71 μ = 2.98 σ = 0.36 b. Weekly work hours: Sarah’s z-score z = + 1.18 μ = 21.6 σ = 7.1 c.

hjlf

Answer:

a) $x = \mu +z*\sigma$

And replacing we got:

$x= 2.98 + 1.71*0.36 = 3.5956$

b) $x = \mu +z*\sigma$

And replacing we got:

$x= 21.6 + 1.18*7.1 = 29.978$

c) $x = \mu -z*\sigma$

And replacing we got:

$x= 150 - 1.35*40= 96$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable of interest for this case. We define the z score with the following formula:

$z=\frac{x-\mu}{\sigma}$