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3 years ago

Solve the proportion 9/12 = 15/a

Mathematics

1 answer:

evablogger [386]3 years ago

3 0

Answer:

a=20

Step-by-step explanation:

You cross multiply: 9a=180

a=20.

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Men outnumber woman in 5 out of the 50 states. In what percent of the states do woman outnumber men?

Naily [24]

Answer:

2.5

Step-by-step explanation:

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3 years ago

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How much must be added to each of the three numbers 1, 11, and 23 so that together they form a geometric progression?

Sliva [168]

Answer:

Step-by-step explanation:

Let x be unknown number which should be added to numbers 1, 11, 23 to get geometric progression. Then numbers 1 + x, 11 + x, 23 + x are first three terms of geometric progression.

Hence,

$b_1=1+x\\ \\b_2=11+x\\ \\b_3=23+x$

and

$b_2=b_1\cdot q\Rightarrow 11+x=(1+x)q\\ \\b_3=b_2\cdot q\Rightarrow 23+x=(11+x)q$

Express q:

$q=\dfrac{11+x}{1+x}=\dfrac{23+x}{11+x}$

Solve this equation. Cross multiply:

$(11+x)^2=(1+x)(23+x)\\ \\121+22x+x^2=23+x+23x+x^2\\ \\121+22x=23+24x\\ \\22x-24x=23-121\\ \\-2x=-98\\ \\2x=98\\ \\x=49$

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3 years ago

(2 tens 1 one)x10 in unit form and standard form

omeli [17]

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

<h3>How to write the number in standard form?</h3>

The number expression is given as:

(2tens 1 one) x 10

2 tens is represented as:

2 * 10

1 one is represented as:

1 * 1

So, the number expression can be rewritten as:

(2tens 1 one) x 10 = (2 * 10 + 1 * 1) x 10

Evaluate the product

(2tens 1 one) x 10 = (20 + 1) x 10

Evaluate the sum

(2tens 1 one) x 10 = (21) x 10

Evaluate the product

(2tens 1 one) x 10 = 210

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

Using the above steps as a guide, we have:

(5 hundreds 5 tens) * 10 ⇒ 5 thousands and 5 hundreds ⇒ 5500
(2 thousands 7 tens) / 10 ⇒ 2 hundreds and 7 units ⇒ 207
(4 ten thousands 8 hundred) / 10 ⇒ 4 thousands and 8 tens ⇒ 4080