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3 years ago

Nine times the sum of a number and 4 is 2

Mathematics

1 answer:

Anna11 [10]3 years ago

7 0

Answer(s):

If you are asking for the equation, it's 9(x+4)=2

However, if you're asking for the value of x as well, it's -34/9

Step by Step:

1) First we must find the equation. In your question, the unknown number is x. Therefore we can know that "the sum of a number and 4" is (x+4). Since we are multiplying this sum by 9, we can put the 9 in front of this expression to multiply it--getting 9(x+4). And since we know it "is 2" we can say that 9(x+4)=2.

2) Now, we have to solve the equation, 9(x+4) = 2

3) We can start by distributing, 9x+36 = 2

4) Now let's move 36 to the right by subtracting from both sides, 9x = -34

5) To isolate x, let's divide both sides by 9, x = -34/9

6) Our fraction answer can't be simplified, so we get x = -34/9

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The monthly earnings of computer systems analysts are normally distributed with a mean of $4,300. If only 1.07% of the systems a

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Answer:800

Step-by-step explanation:

$Mean(\mu )=\$ 4300$

and $P(X>6140)=0.0107$

$P(X>x_0)=0.0107$

$P\left ( \frac{X-\mu }{\sigma}$

$P\left ( z$

$\frac{x-\mu }{\sigma}=InvNormal(0.9893)$

Using Z table to get InvNormal(0.9893)=2.30

$\frac{6140-4300}{\sigma}=2.30$

$\sigma =\frac{6140-4300}{2.30}=800$

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4 years ago

Read 2 more answers

Suppose you are given either a fair dice or an unfair dice (6-sided). You have no basis for considering either dice more likely

hoa [83]

Answer: Our required probability is 0.83.

Step-by-step explanation:

Since we have given that

Number of dices = 2

Number of fair dice = 1

Probability of getting a fair dice P(E₁) = $\dfrac{1}{2}$

Number of unfair dice = 1

Probability of getting a unfair dice P(E₂) = $\dfrac{1}{2}$

Probability of getting a 3 for the fair dice P(A|E₁)= $\dfrac{1}{6}$

Probability of getting a 3 for the unfair dice P(A|E₂) = $\dfrac{1}{3}$

So, we need to find the probability that the die he rolled is fair given that the outcome is 3.

So, we will use "Bayes theorem":

$P(E_1|A)=\dfrac{P(E_1)P(A|E_1)}{P(E_1)P(A|E_1)+P(E_2)P(A|E_2)}\\\\(E_1|A)=\dfrac{0.5\times 0.16}{0.5\times 0.16+0.5\times 0.34}\\\\P(E_1|A)=0.83$

Hence, our required probability is 0.83.

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3 years ago

A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108

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Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

$4x+L=108$

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

$V=x^2L$

If we express L in function of x using the restriction equation, we get:

$4x+L=108\\\\L=108-4x$

We replace L in the volume formula and we get

$V=x^2L=x^2*(108-4x)=-4x^3+108x^2$

To maximize the volume we derive and equal to 0

$\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18$

We can replace x to calculate L:

$L=108-4x=108-4*18=108-72=36$

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

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3 years ago

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Given the 5th term is 103 and the come differences is -6 2/3 what is the 6th term?

LekaFEV [45]

Answer:

102 1/3

Step-by-step explanation:

To find the 6th term, add the common difference to the 5th term:

103 + (-6 2/3) = 102 1/3

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4 years ago

The coordinates of the vertices of ANGLE RST are R(-3,5), and S(4,5), and T(4,-2). Find the side lengths to the nearest hundredt

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Side lengths: RS=7 and ST=7, and angle=90 degrees

Why?

Since second coordinates of R and S are the same so we can just count the length by adding first coordinate of R and first coordinate of S= |-3|+4=7

Since first coordinates of R is the same as first coordinate of T so we can just count the length by adding second coordinates of S and T=5+|-2|=7

Angle: RST is =90 degrees because triangle RST is right angled triangle. Why? Because RS is parallel to X axis(the same second coordinates of R and S) and ST is parallel to Y axis(the same coordinates of S and T) .

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3 years ago