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Bogdan [553]
3 years ago
13

Apply the rules for order of operstions to simplify 2 + 3 - 4 (5 × 4)

Mathematics
1 answer:
Lerok [7]3 years ago
7 0
Just use PEMDAS 
2+3-4 (5x4) 

Parenthesis
Exponents 
Multiplication
Division
Addition 
Subtraction    So first is Parenthesis 5x4=20 next will be Addition because there are no exponents 2+3= 5-4= 1 so now we go back to multiplication 20 x 1= 20 so 20 is your answer. 

Hope I helped out ^^


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Law Incorporation [45]

Answer:

Magnitude =\sqrt{59} \\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}

Step-by-step explanation:

A=2i+3j+4k

B=i-2j+3k

Sum of the vectors:

A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k

Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\Magnitude =\sqrt{9+1+49} \\\\Magnitude =\sqrt{59}

Direction of the sum of the vectors:

\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\

3 0
2 years ago
Slope intercept form of a line that has a slope of -3/4 and passes through (4, 3)
tia_tia [17]
<h3><u>Explanation</u></h3>
  • First Method

We have the given slope value and the coordinate point that the graph passes through.

y = mx + b

where m = slope and b = y-intercept. Substitute the value of slope in the equation.

y =  -  \frac{3}{4} x + b

We have the given coordinate point as well. After we substitute the slope, we substitute the coordinate point value in the equation.

3 =  -  \frac{3}{4} (4) + b \\

<u>Solve</u><u> </u><u>the</u><u> </u><u>equation</u><u> </u><u>for</u><u> </u><u>b-term</u>

3 =  - 3 + b \\ 3 + 3 = b \\ 6 = b

The value of b is 6. We substitute the value of b in the equation.

y =  -  \frac{3}{4} x + 6

  • Second Method

We can also use the Point-Slope form to solve the question.

y - y_1 = m(x - x_1)

Given the y1 and x1 = the coordinate point value.

Substitute the slope and coordinate point value in the point slope form.

y - 3 = -  \frac{3}{4} (x - 4)

<u>Simplify</u><u>/</u><u>Convert</u><u> </u><u>into</u><u> </u><u>Slope-intercept</u>

y =  -  \frac{3}{4} (x - 4) + 3 \\ y =  -  \frac{3}{4} x +  \frac{12}{4}  + 3 \\ y =  -  \frac{3}{4} x + 3 + 3 \\y =  -  \frac{3}{4} x + 6

<h3><u>Answer</u></h3>

<u>\large \boxed {y =  -  \frac{3}{4} x + 6}</u>

6 0
3 years ago
The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15.
evablogger [386]

Answer:

4.4% of the population with IQ between 120 and 125.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.

a) Let X be a person's IQ score.

Then, density functions for IQ scores is given by:

P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{z^2}{2}}\\\\\text{where,}\\\\z = \frac{x-\mu}{\sigma}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-100)^2}{450}}

b) P(population with IQ between 120 and 125.)

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

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Step-by-step explanation:

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3 years ago
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Darina [25.2K]

Answer: 3400

Step-by-step explanation:

We have, 5% × x = 170

or,  

5

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× x = 170

Multiplying both sides by 100 and dividing both sides by 5,

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5

x = 3400

If you are using a calculator, simply enter 170×100÷5, which will give you the answer.

4 0
3 years ago
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