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3 years ago

GIVING BRAINLIEST Try the numbers 4, 5, 6, 7 in the equation 6 ⋅ x + 5 = 12 + 5 ⋅ x

Mathematics

1 answer:

Harrizon [31]3 years ago

6 0

<h3>6 is a solution to equation 6x + 5 = 12 + 5x</h3>

Solution:

Given equation is:

6x + 5 = 12 + 5x

Try the numbers 4, 5, 6, 7 in the equation to test whether any of them is a solution

Substitute x = 4

6(4) + 5 = 12 + 5(4)

24 +5 = 12 + 20

$29 \neq 32$

Thus 4 is not a solution

Substitute x = 5

6(5) + 5 = 12 + 5(5)

30 + 5 = 12 + 25

$35\neq 37$

Thus 5 is not a solution

Substitute x = 6

6(6) + 5 = 12 + 5(6)

36 + 5 = 12 + 30

$41\neq 42$

Thus 6 is not a solution

Substitute x = 7

6(7) + 5 = 12 + 5(7)

42 + 5 = 12 + 35

47 = 47

Thus 6 is a solution

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3 years ago

Please help!! Needed ASAP!!

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3 years ago

2. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. a. Would you

ANEK [815]

Answer:

Step-by-step explanation:

Size of the population, N = 4000

Size of the sample, n = 40

n/N = 40/4000 = 0.01

0.01 is less than 0.05 and hence we would not us the finite population correction factor in calculating the standard error of the mean.

Population standard deviation is σ = 8.2

So, the standard error of x’ using the finite population correction factor is give by

σ(x’) = √[(N - n)/(N - 1)] x (sigma/√n)

σ(x’) = √[(4000 - 40)/(4000 - 1)] x (8.2/√40)

σ(x’) = 1.29

Standard error of x’ without using the finite population correction factor is

σ(x’) = σ/√n

σ(x’) = 8.2/√40 = 1.2965

There is little difference between the two values of the standard error. So we can ignore the population correction factor.

Let the population mean be μ

Probability that the sample mean will be within =-2 of the population mean is

P(μ– 2 < x’ < μ + 2)

At x’ = μ – 2 , we have

z = (μ – 2 – μ)/1.2965

z = -1.54

at x’ = μ + 2, we have

z = (μ + 2 – μ)/1.2965

z = 1.54

So the required probability is

P(μ – 2 < x’ < μ + 2) = p(-1.54< z < 1.54)

P(μ – 2 < x’ < μ + 2) = p(z < 1.54) – p(z < -1.54)

P(μ – 2 < x’ < μ + 2) = 0.9382 – 0.0618

P(μ – 2 < x’ < μ + 2) = 0.8764

7 0

3 years ago

english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with th

Valentin [98]

The words need not be English language words 142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters then it is just 26-choose-5 or (26/5).

If the word has 4 different letters then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives = 4*(26/4)

If the word has 3 different letters then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives = 6*(26/3).

If the word has 2 different letters then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is = 4*(26/2).

The word has just 1 distinct letter you have = (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) + (26/1)

= 142506

The words need not be English language words = 142506

Learn more about permutation and combination

brainly.com/question/28065038

#SPJ4

5 0

1 year ago

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for x.)

marshall27 [118]

The volume of the composite figure is the third option 385.17 cubic centimeters.

Step-by-step explanation:

Step 1:

The composite figure consists of a cone and a half-sphere on top.

We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.

The radius is 4 cm and the height is 15 cm.

The volume of the cone :

$V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32$ cubic cm.

Step 3:

The area of a half-sphere is half of a full sphere.

The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 4 cm. We take π as 3.1415.

The volume of a full sphere $\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07$ cubic cm.

The volume of the half-sphere $=\frac{1}{2} (268.07) = 134.037$ cubic cm.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume $251.32+134.037 = 385.357$ cub cm. This is closest to the third option 385.17 cubic centimeters.

5 0

4 years ago