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2 years ago

" title="\frac{1}{2} - x + \frac{3}{4} = x - 4" alt="\frac{1}{2} - x + \frac{3}{4} = x - 4" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Rasek [7]2 years ago

7 0

Answer:

$x = \dfrac{21}8$

Step-by-step explanation:

$~~~~~~~~\dfrac 1 2 -x + \dfrac 34 = x-4\\\\\\\implies \dfrac 24 + \dfrac 34 - x =x-4\\\\\\\implies \dfrac 54+4=x+x\\\\\\\implies 2x = \dfrac{21}{4}\\\\\\\implies x = \dfrac{21}{4 \cdot 2}\\\\\\\implies x = \dfrac{21}8$

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The scores on a test are normally distributed with a mean of 110 and a standard deviation of 22. What is the score that is 3 sta

Alborosie

Answer:

Step-by-step explanation:

If the mean is 110, and the standard devaition is 22,

1 standard dev. below the mean is 110-22

2 standard dev below the mean is 110-22-22

3 standard dev below the mean is 110-22-22-22

Hope that helps!

7 0

4 years ago

What’s the answer I will do 50 points first person to answer

SSSSS [86.1K]

Answer: 1. Route ABC is a right triangle.

2. Route CDE ia not a right triangle.

3. Distance HJ= 23.32miles

4. Distance GE = 17

5. Missing length= 35

6. The sides 16, 60, 62 do NOT belong to a right triangle.

Step-by-step explanation:

Going by Pythagoras theorem, for triangle to be proven to be a right triangle, the condition below must be satisfied.

Hypotenuse² = Opposite² + Adjacent²

For question 1,

Hyp =13, opp = 5, Adj is 12

Going by Pythagoras rule.

Since 13²= 5² + 12²

Then triangle ABC is a right triangle.

For question 2,

Using the same Pythagoras theorem to prove,

In triangle CDE,

Hyp= 22, opp= 18, Adj = 14

Since 22² is not = 18² + 14²

then CDE is not a right triangle.

For question 3,

For triangle HIJ, since it is confirmed to be a right triangle, then we use the Pythagoras theorem to calculate the missing side.

Longest side if the triangle= IJ = hypotenuse = 25

HI = 9.

IJ² = HI² + HJ²

HJ²= IJ² - HI²

HJ² = 25² - 9²

HJ² = 625 - 81

HJ= √544

HJ = 23.32miles

For question 4,

FGE is also shown to be a right triangle and the missing side GE is the longest side which is also the hypotenuse.

FG= 8, FE =15

Using the Pythagoras theorem,

Hyp² = FG² + FE²

GE² = 8² + 15²

GE² = 289

GE = √289

GE = 17.

For question 5,

The hypotenuse is given as 37, one side is given as 12, let's call the missing side x

Going by Pythagoras theorem,

37² = 12²+ x²

x²= 37² - 12²

x²= 1225

x=√1225

x=35.

The missing side is 35inches.

For number 6,

The numbers given are 16, 60, 62

To know if three sides belong to a right angle, we simply put them to test using Pythagoras theorem.

It is worthy of note that the longest side is the hypotenuse.

This brings us to the equation to check below that since:

62² Is not = 60² + 16²

Then the side lengths 16, 60, 62 do not belong to a right angle.

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4 years ago

An online furniture store sells chairs for $50 each and tables for $550 each. Every day, the store can ship a maximum of 20 piec

Leya [2.2K]

Answer:

If 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.

Step-by-step explanation:

Selling price of each table = $50

Selling price of each table = $550

Let the number of chairs sold in a a day = x

Let Number of tables old in a a day = y

Hence, the selling price of x chairs = x times $50 = 50 x

and the selling price of y tables = y times $550 = 550 y

Maximum number of pieces that can be shipped = 20

⇒ x + y ≤ 20

Also, The total selling amount should at least be $5,000

⇒ 50 x + 550 y ≥ 5,000

Hence, the given system of equation is:

x + y ≤ 20

50 x + 550 y ≥ 5,000

Solving the given system:

put y = 20 - x from (1) in the equation (2), we get

50 x + 550 y = 5,000 ⇒ 50x + 550(20 -x) = 5000

or, 50x + 11,000 - 550x = 5000

or, -500x = -6000

x = 12

or the number of chairs sold at maximum = 12

also, y = 20- x = 20 - 12 = 8

So, number of tables sold at maximum = 8

Now, if the number of chairs sold = 9,

then the number of tables sold = 20 - 9 = 11

The selling amount is 50(9) + 550(11) = $6,500 > $5,000

Hence, 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.

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4 years ago

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Step-by-step explanation:

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3 years ago

A sample of 12 measurements has a mean of 16.5, and a sample of 15 measurements has a mean of 18.6. Find the mean of all 27 meas

Wewaii [24]

Answer: $17.67$

Step-by-step explanation:

Given

Sample of 12 measurements has a mean of 16.5 and

a sample of 15 measurements has a mean of 18.6

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and $\bar{x_2},n_2$ be the mean and no of measurements in second case

$\therefore \bar{x_1}=\dfrac{\sum a_1}{n_1}\\\\\Rightarrow \sum a_1=\bar{x_1}\times n_1\\\\\Rightarrow \sum a_1=198\quad \ldots(1)$

Similarly,

$\therefore \bar{x_2}=\dfrac{\sum a_2}{n_2}\\\\\Rightarrow \sum a_2=\bar{x_2}\times n_2\\\\\Rightarrow \sum a_2=279\quad \ldots(2)$

Mean of 27 measurements

$\Rightarrow \bar{x_3}=\dfrac{\sum a_1+\sum a_2}{n_1+n_2}\\\\\Rightarrow \bar{x_3}=\dfrac{198+279}{12+15}\\\\\Rightarrow \bar{x_3}=\dfrac{477}{27}\\\\\Rightarrow \bar{x_3}=17.67$

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3 years ago