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3 years ago

How do I solve for e? 9e+4=-5e+14+13e

Mathematics

2 answers:

Zina [86]3 years ago

8 0

Answer:

$e=10$

Step-by-step explanation:

$9e+4=-5e+14+13e$

Simplify both sides by combining $-5e+13e$ :

$9e+4=8e+14$

Isolate the variable e. Subtract 8e from both sides:

$9e-8e+4=8e-8e+14\\\\e+4=14$

Subtract 4 from both sides:

$e+4-4=14-4\\\\e=10$

:Done

IrinaVladis [17]3 years ago

7 0

Answer: e = 10

Step-by-step explanation: 9e + 4 = -5e + 14 + 13 e

Now lets bring the variables and numbers on a different side

Remember that when the numbers go to the other side the sign changes

so 4 - 14 = -9e + 13e -5e

-10 = -e

10 = e

if plug in both equations on a graph then you will see that when e = 10 the lines meet at 94.

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For each value of y , determine whether it is a solution to -21=6y-9 . A -5, B 3 , C -2, D 9

Nezavi [6.7K]

Option C

For each value of y, -2 is a solution of -21 = 6y - 9

Solution:

Given, equation is – 21 = 6y – 9

We have to find that whether given set of options can satisfy the above equation or not

Now, let us check one by one option

Option A)

Given option is -5

Let us substitute -5 in given equation

- 21 = 6(-5) – 9

- 21 = -30 – 9

- 21 = - 39

L.H.S ≠ R.H.S ⇒ not a solution

Option B)

Given option is 3

- 21 = 6(3) – 9

- 21 = 18 – 9

- 21 = 9

L.H.S ≠ R.H.S ⇒ not a solution

Option C)

Given option is -2

- 21 = 6(-2) – 9

- 21 = - 12 – 9

- 21 = - 21

L.H.S = R.H.S ⇒ yes a solution

Option D)

- 21 = 6(9) – 9

- 21 = 54 – 9

- 21 = 45

L.H.S ≠ R.H.S ⇒ not a solution

Hence, the solution for the given equation is – 2, so option c is correct

6 0

4 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat

dimulka [17.4K]

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the 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 and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ - 5.18) /0.07

=> 0.1036 = x₁ - 5.18