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2 years ago

Orin solved an equation and justified his steps as shown in the table.

Mathematics

1 answer:

sergij07 [2.7K]2 years ago

6 0

Answer:

Step-by-step explanation:

Given the equation as

$\frac{3x}{5} -3=12$

apply multiplication property of equality where you multiply every term by 5

$\frac{3x}{5}*5 -3*5=12*5$

3x-15=60------------------apply addition property of equality

3x-15+15=60+15

3x=75--------------------------appy division property of equality by dividing both sides by 3

3x/3=75/3

x=25

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An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

gregori [183]

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial probability distribution because:

In the question it is given that the sprinklers activate correctly or not independently.
The number of outcomes are two i.e. sprinklers activate correctly or not.

A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

b = binomial probability also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

$C_{n,x}$ is calculated as:

$C_{n,x}$ = n! / x!(n – x)!

= 10! / 10!(10-10)!

= 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

= 1 * 0.0282 * (0.3) ⁰

= 1 * 0.0282 * 1

P(X=x) = 0.0282

5 0

1 year ago

Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl i

jarptica [38.1K]

Answer:

Bianca's height = 42 inches

Step-by-step explanation:

Let x be the Bianca height.

Given:

Meredith height = 60 inches

We need to find the Bianca height.

Solution:

From the given statement the Meredith's height is $\frac{2}{3}$ of Bianca's height plus 32 inches, so the equation is.

Meredith's height = $\frac{2}{3}(Bianca\ height)+32$

Substitute Meredith's height in above equation.

$60=\frac{2}{3}x+32$

Now we solve the above equation for x.

$\frac{2}{3}x=60-32$

$\frac{2}{3}x=28$

By cross multiplication.

$x=\frac{3\times 28}{2}$

28 divided by 2.

$x= 3\times 14$

$x=42\ in$

Therefore, the height of the Bianca is 42 inches.

7 0

1 year ago

Mr robbins earns a commission on each airfare he books. At the end of the day,he had booked $208.60 worth if airfare and earned

LenKa [72]

Answer:

Mr. Robins commision rate is 15%.

Step-by-step explanation:

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

Mr robbins earns a commission on each airfare he books.

At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.

Here

Part value = $31.29

Total value = $208.60

Put in the formula

$Percentage = \frac{31.29\times 100}{208.60}$

$Percentage = \frac{312900}{20860}$

Percentage = 15%

Therefore the Mr. Robins commision rate is 15%.

4 0

2 years ago

Which statements can be represented by this equation? Select three options.

mars1129 [50]

Answer:

Options A,C and E.

Step-by-step explanation:

The given equation is

$2n-9.2=n+\dfrac{4}{5}$

Let n be the unknown number, then

Twice a number minus nine and two-tenths is the same as the number plus four-fifths.

$2n-9.2=n+\dfrac{4}{5}$

So, option A is correct.

Nine point two decreased by double a number is the same as the number added to four-fifths.

$9.2-2n=n+\dfrac{4}{5}$

Nine point two less than twice a number is equal to the number added to four-fifths.

$2n-9.2=n+\dfrac{4}{5}$

So, option C is correct.

Two times the difference of a number and nine and two-tenths is equal to the number plus four-fifths.

$2(n-9.2)=n+\dfrac{4}{5}$

Double a number decreased by nine and two-tenths is the same as the sum of four-fifths and the number.

$2n-9.2=n+\dfrac{4}{5}$

So, option E is correct.

Therefore, the correct options are A,C and E.

5 0

2 years ago

Read 2 more answers

The exchange rate at the post office is £1=€1.17 how many euros will you get for £280

4vir4ik [10]

Question

The exchange rate at the post office is £1=€1.17 how many euros will you get for £280

Answer:

Step-by-step explanation:

you can solve with an equation

1£ : 1.17€ = 280£ : x

1 : 1.17 = 280 : x

x = 1.17 * 280 : 1

x = 327.6

-------------------

check

1 : 1.17 = 280 : 327.6

0.85 = 0.85

the answer is good

------------------------------------

or you can simpy solve with a multiplication

280 * 1.17 = 327.6

4 0

1 year ago