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Stella [2.4K]
3 years ago
9

A small garden measures 8 ft by 7 ft. A uniform border around the garden increases the total area to 110 ft 2. What is the width

of the border?
Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer: 3

Step-by-step explanation:

You can answer this question by using the equation

(8+x)(7+x)=110

The x represents the width, as we do not know the area. If you simplify the equation, it becomes 56+15x+x2=110.

If you move all the terms to the left side, and rearrange it, it can become x^2+15x-54=0

This can be simplified into (x-3)(x+18)=0

This equation makes it so that x is either 3 or -18. It is not possible for a width to be -18, so the width must be 3.

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Suppose a large shipment of telephones contained 21% defectives. If a sample of size 498 is selected, what is the probability th
grandymaker [24]

Answer:

P(-3\% < x < 3\%) = 0.901

Step-by-step explanation:

Given

p = 21\%

n = 498

Required

P(-3\% < x < 3\%)

First, we calculate the z score

z = \sqrt{p * (1 - p)/n}

z = \sqrt{21\% * (1 - 21\%)/498}

z = \sqrt{21\% * (79\%)/498}

z = \sqrt{0.1659/498}

z = \sqrt{0.000333}

z = 0.0182

So:

P(-3\% < x < 3\%) = P(-3\%/0.0182 < z

P(-3\% < x < 3\%) = P(1.648 < z

From z probability, we have:

P(-3\% < x < 3\%) = 0.901

6 0
2 years ago
..................................
yanalaym [24]

Answer:

The answer is a² .

Step-by-step explanation:

You have to substitute x and y into the expression :

let \: x = a \cos(θ) \\ let \: y = a \sin( θ)

{x}^{2}  +  {y}^{2}  =  {(a \cosθ )}^{2}  +  {(a \sinθ) }^{2}

{x}^{2}  +  {y}^{2}  =  {a}^{2}( {cos}^{2}θ) +  {a}^{2} ({sin}^{2}θ)

Next, you have to apply Basic Trigonometric Identity :

{sin}^{2} θ +  {cos}^{2} θ = 1

{x}^{2}  +  {y}^{2}  =  {a}^{2} ( {cos}^{2} θ +  {sin}^{2} θ)

{x}^{2}  +  {y}^{2}  =  {a}^{2} (1)

{x}^{2}  +  {y}^{2}  =  { a}^{2}

8 0
3 years ago
X^4=15 <br> is an exponential equation?
miskamm [114]

Answer:

No. It is not an Exponential Equation.

Step-by-step explanation:

Givenx^{4} =15

By the Definition of Exponential Equation which states.

"The equation is said to be an exponential equation when it has a variable occurred in the exponent and which have the same base."

For Example:

All given below are said to be exponential equations.

5^{x} =5^{2} \\7^{x}=49\\

which can be rewritten as

7^{x}=7^{2}

Now in the given equation x^{4}=15 it doesn't have same base neither any means the base can be made same,hence the given equation is not an exponential equation

8 0
3 years ago
Difference 77/8 -31/4=
ad-work [718]
The answer is 15/8 
simplified: 1  7/8
3 0
2 years ago
Read 2 more answers
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sattari [20]

We don't know what WCLM means or have any contacts clues

8 0
3 years ago
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